{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0001","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ab01d738d8394fd65988c57ea039fbb06a706d54988f7b8adfee8525a40547e","family_id":"qf-distance-coordinate","seed":20260912,"semantic_template":"qf-distance-coordinate/20260912"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-23, -26) and Q=(-20, -22). Find the distance d(P,Q).","answer":{"kind":"numeric","value":5,"explanation":"The coordinate difference is (3, 4), so d=√((3)²+(4)²)=5."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0002","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d7d29ad948ddeae6962cffdb02e64ef90adc2c84023a605d4e202dfdb882af9","family_id":"qf-distance-coordinate","seed":20260913,"semantic_template":"qf-distance-coordinate/20260913"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-16, -15) and Q=(-21, -3). Find the distance d(P,Q).","answer":{"kind":"numeric","value":13,"explanation":"The coordinate difference is (-5, 12), so d=√((-5)²+(12)²)=13."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0003","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00c72ac70baf02e0823e8a19b914029db3cc72a262f19c78dd4c0f4685d598d9","family_id":"qf-distance-coordinate","seed":20260914,"semantic_template":"qf-distance-coordinate/20260914"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-9, -4) and Q=(-1, -19). Find the distance d(P,Q).","answer":{"kind":"numeric","value":17,"explanation":"The coordinate difference is (8, -15), so d=√((8)²+(-15)²)=17."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0004","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b6ecd35e724fe7a6940daa19c1a6c125e0884128c9d528861f2dbf177284b63","family_id":"qf-distance-coordinate","seed":20260915,"semantic_template":"qf-distance-coordinate/20260915"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-2, 7) and Q=(-9, -17). Find the distance d(P,Q).","answer":{"kind":"numeric","value":25,"explanation":"The coordinate difference is (-7, -24), so d=√((-7)²+(-24)²)=25."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0005","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9029658eb223d4663700189b383f680bac319aa1bab9c905ebcef786e06333b6","family_id":"qf-distance-coordinate","seed":20260916,"semantic_template":"qf-distance-coordinate/20260916"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(5, 18) and Q=(25, 39). Find the distance d(P,Q).","answer":{"kind":"numeric","value":29,"explanation":"The coordinate difference is (20, 21), so d=√((20)²+(21)²)=29."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0006","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0538f0decc00c3c49e5b27ee33d7e75bda22f97985578b49f78bb43b028a694e","family_id":"qf-distance-coordinate","seed":20260917,"semantic_template":"qf-distance-coordinate/20260917"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(12, -24) and Q=(3, 16). Find the distance d(P,Q).","answer":{"kind":"numeric","value":41,"explanation":"The coordinate difference is (-9, 40), so d=√((-9)²+(40)²)=41."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0007","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a3e88ae82f7b21b24cafc5a49d170c074b6ae44716736f49f755fac1fb1d118","family_id":"qf-distance-coordinate","seed":20260918,"semantic_template":"qf-distance-coordinate/20260918"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(19, -13) and Q=(31, -48). Find the distance d(P,Q).","answer":{"kind":"numeric","value":37,"explanation":"The coordinate difference is (12, -35), so d=√((12)²+(-35)²)=37."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0008","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ecff48f00b86f1ae703fc8ac6cb3f1883944ce2299b5e5248f089ad7f771ba2","family_id":"qf-distance-coordinate","seed":20260919,"semantic_template":"qf-distance-coordinate/20260919"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-21, -2) and Q=(-32, -62). Find the distance d(P,Q).","answer":{"kind":"numeric","value":61,"explanation":"The coordinate difference is (-11, -60), so d=√((-11)²+(-60)²)=61."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0009","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ea4566fbc7d7d274848c598447394a1d4fe7ccb6ab22b82d5c186e474648a26","family_id":"qf-distance-coordinate","seed":20260920,"semantic_template":"qf-distance-coordinate/20260920"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-14, 9) and Q=(14, 54). Find the distance d(P,Q).","answer":{"kind":"numeric","value":53,"explanation":"The coordinate difference is (28, 45), so d=√((28)²+(45)²)=53."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0010","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e2a3a3bf32146a9c6d556228fb07e997d098eef8569cf261c89ebc72b6d179b","family_id":"qf-distance-coordinate","seed":20260921,"semantic_template":"qf-distance-coordinate/20260921"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-7, 20) and Q=(-40, 76). Find the distance d(P,Q).","answer":{"kind":"numeric","value":65,"explanation":"The coordinate difference is (-33, 56), so d=√((-33)²+(56)²)=65."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0011","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5d4fa262a533f1dcd7c1130e71851a250d78b75e69ec17f9f66bda79c77157e","family_id":"qf-distance-coordinate","seed":20260922,"semantic_template":"qf-distance-coordinate/20260922"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(0, -22) and Q=(16, -85). Find the distance d(P,Q).","answer":{"kind":"numeric","value":65,"explanation":"The coordinate difference is (16, -63), so d=√((16)²+(-63)²)=65."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0012","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c69d53e0ff167209736386aaf032519119207e248e8c0bc731c05c9e7639b32d","family_id":"qf-distance-coordinate","seed":20260923,"semantic_template":"qf-distance-coordinate/20260923"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(7, -11) and Q=(-41, -66). Find the distance d(P,Q).","answer":{"kind":"numeric","value":73,"explanation":"The coordinate difference is (-48, -55), so d=√((-48)²+(-55)²)=73."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0013","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5bc42abba2e4540cc58aaa6ae9bec6f73f4970d070d8c1846d182e4bf39b9ca","family_id":"qf-distance-coordinate","seed":20260924,"semantic_template":"qf-distance-coordinate/20260924"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(14, 0) and Q=(27, 84). Find the distance d(P,Q).","answer":{"kind":"numeric","value":85,"explanation":"The coordinate difference is (13, 84), so d=√((13)²+(84)²)=85."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0014","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d88f116b5fb249662312ed4ca0f9eb11ba4becbd58204b7cc65e0c9e99313c3","family_id":"qf-distance-coordinate","seed":20260925,"semantic_template":"qf-distance-coordinate/20260925"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(21, 11) and Q=(-15, 88). Find the distance d(P,Q).","answer":{"kind":"numeric","value":85,"explanation":"The coordinate difference is (-36, 77), so d=√((-36)²+(77)²)=85."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0015","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ba238a1d0606ff39e14380071594fd79d1e38b9c3beeaffb07ab7f21ba5bb9b","family_id":"qf-distance-coordinate","seed":20260926,"semantic_template":"qf-distance-coordinate/20260926"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-19, 22) and Q=(20, -58). Find the distance d(P,Q).","answer":{"kind":"numeric","value":89,"explanation":"The coordinate difference is (39, -80), so d=√((39)²+(-80)²)=89."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0016","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca88d4875457f3c017a20118ba9772a871527a6da82f8f4e0d7e5c56566404d0","family_id":"qf-distance-coordinate","seed":20260927,"semantic_template":"qf-distance-coordinate/20260927"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-12, -20) and Q=(-77, -92). Find the distance d(P,Q).","answer":{"kind":"numeric","value":97,"explanation":"The coordinate difference is (-65, -72), so d=√((-65)²+(-72)²)=97."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0017","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"107fcfd2bb5ef07f03325ae52f9fa72b801b129b5472377d1c8c3e085d6b7eea","family_id":"qf-distance-coordinate","seed":20260928,"semantic_template":"qf-distance-coordinate/20260928"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-5, -9) and Q=(15, 90). Find the distance d(P,Q).","answer":{"kind":"numeric","value":101,"explanation":"The coordinate difference is (20, 99), so d=√((20)²+(99)²)=101."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0018","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96c79ea221d84741dfc75d708c4f77bf4dda8ec526412c9ec3a35f2b3aa1438c","family_id":"qf-distance-coordinate","seed":20260929,"semantic_template":"qf-distance-coordinate/20260929"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(2, 2) and Q=(-58, 93). Find the distance d(P,Q).","answer":{"kind":"numeric","value":109,"explanation":"The coordinate difference is (-60, 91), so d=√((-60)²+(91)²)=109."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0019","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"06d1a48830a49aed1a5ceb826b2a8dcc0a9bc47083b426b7a334a609459e57d5","family_id":"qf-distance-coordinate","seed":20260930,"semantic_template":"qf-distance-coordinate/20260930"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(9, 13) and Q=(24, -99). Find the distance d(P,Q).","answer":{"kind":"numeric","value":113,"explanation":"The coordinate difference is (15, -112), so d=√((15)²+(-112)²)=113."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0020","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d1f359aa353757e9a2f0605c3b17fba6a88bb2aebc419c33333bc2ad2f4e776","family_id":"qf-distance-coordinate","seed":20260931,"semantic_template":"qf-distance-coordinate/20260931"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(16, 24) and Q=(-28, -93). Find the distance d(P,Q).","answer":{"kind":"numeric","value":125,"explanation":"The coordinate difference is (-44, -117), so d=√((-44)²+(-117)²)=125."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0021","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e1ccbfd04977c87c909e5d431bbf0e11b58cbdb48ebcdf2fdd8671f4032a6e33","family_id":"qf-distance-coordinate","seed":20260932,"semantic_template":"qf-distance-coordinate/20260932"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(23, -18) and Q=(29, -10). Find the distance d(P,Q).","answer":{"kind":"numeric","value":10,"explanation":"The coordinate difference is (6, 8), so d=√((6)²+(8)²)=10."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0022","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9876909e2d0b799f395dfa8117cf2a03da954b3ef4491338838051c5c111edc","family_id":"qf-distance-coordinate","seed":20260933,"semantic_template":"qf-distance-coordinate/20260933"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-17, -7) and Q=(-27, 17). Find the distance d(P,Q).","answer":{"kind":"numeric","value":26,"explanation":"The coordinate difference is (-10, 24), so d=√((-10)²+(24)²)=26."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0023","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64ce7499f5ed9d46f194c0f0a89157e534f7011ad8886efa45b5cd877b5ee641","family_id":"qf-distance-coordinate","seed":20260934,"semantic_template":"qf-distance-coordinate/20260934"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-10, 4) and Q=(6, -26). Find the distance d(P,Q).","answer":{"kind":"numeric","value":34,"explanation":"The coordinate difference is (16, -30), so d=√((16)²+(-30)²)=34."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0024","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5893b341331564bbb8a60f2a731c63b50fe6874d8704ec8236f2a3b5fc72df6","family_id":"qf-distance-coordinate","seed":20260935,"semantic_template":"qf-distance-coordinate/20260935"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-3, 15) and Q=(-17, -33). Find the distance d(P,Q).","answer":{"kind":"numeric","value":50,"explanation":"The coordinate difference is (-14, -48), so d=√((-14)²+(-48)²)=50."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0025","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d21f8fbba657768c73031a39529f76488953fe506858c234f34367d9f6b8ce1e","family_id":"qf-distance-coordinate","seed":20260936,"semantic_template":"qf-distance-coordinate/20260936"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(4, 26) and Q=(44, 68). Find the distance d(P,Q).","answer":{"kind":"numeric","value":58,"explanation":"The coordinate difference is (40, 42), so d=√((40)²+(42)²)=58."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0026","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"577c0bfe69890027ec976451a5798253cf96df263500ebb636e56c6fc3c9c9ac","family_id":"qf-distance-coordinate","seed":20260937,"semantic_template":"qf-distance-coordinate/20260937"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(11, -16) and Q=(-7, 64). Find the distance d(P,Q).","answer":{"kind":"numeric","value":82,"explanation":"The coordinate difference is (-18, 80), so d=√((-18)²+(80)²)=82."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0027","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"008a7f9d8b11b17a22a08ec58b01810bebe49a94a13bdfff92d8d5021c99dca5","family_id":"qf-distance-coordinate","seed":20260938,"semantic_template":"qf-distance-coordinate/20260938"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(18, -5) and Q=(42, -75). Find the distance d(P,Q).","answer":{"kind":"numeric","value":74,"explanation":"The coordinate difference is (24, -70), so d=√((24)²+(-70)²)=74."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0028","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"243818a084ce061a6e60cd2d1c5f72c6e154a137443458dae68962f230d4766b","family_id":"qf-distance-coordinate","seed":20260939,"semantic_template":"qf-distance-coordinate/20260939"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-22, 6) and Q=(-44, -114). Find the distance d(P,Q).","answer":{"kind":"numeric","value":122,"explanation":"The coordinate difference is (-22, -120), so d=√((-22)²+(-120)²)=122."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0029","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc92acb2e7058d1f7a6aa382483029efec20549d11897127d35c3fb59f8fd741","family_id":"qf-distance-coordinate","seed":20260940,"semantic_template":"qf-distance-coordinate/20260940"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-15, 17) and Q=(41, 107). Find the distance d(P,Q).","answer":{"kind":"numeric","value":106,"explanation":"The coordinate difference is (56, 90), so d=√((56)²+(90)²)=106."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-distance-coordinate-0030","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07c0416627cbc34bc595ae6911139695a17bade3aec3dc3a88404c03cc9646bb","family_id":"qf-distance-coordinate","seed":20260941,"semantic_template":"qf-distance-coordinate/20260941"},"fields":{"title":"Coordinate-Plane Distance","stem":"In the Euclidean plane, P=(-8, -25) and Q=(-74, 87). Find the distance d(P,Q).","answer":{"kind":"numeric","value":130,"explanation":"The coordinate difference is (-66, 112), so d=√((-66)²+(112)²)=130."},"skills":["coordinate differences","distance formula"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0001","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29e49835783efd0dd0f040c2fa2e86e950ca926c1b0bbeac22f2f2ef8982cc05","family_id":"qf-right-triangle-determination","seed":20260942,"semantic_template":"qf-right-triangle-determination/20260942"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 10°, 90°, 80°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0002","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e906b62bf5691d78aea8fe378f6de337a15b0bfb62a50bd90cc37dc7f3e7954","family_id":"qf-right-triangle-determination","seed":20260943,"semantic_template":"qf-right-triangle-determination/20260943"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 15°, 80°, 85°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0003","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9878ffa9d095b34a589c67215b218c9ec42eedff086cfe32ed61520f04faec1a","family_id":"qf-right-triangle-determination","seed":20260944,"semantic_template":"qf-right-triangle-determination/20260944"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 20°, 90°, 70°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0004","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"22d889ee2968c87aa10aa3c9ce633ef8c7a470ace97721851b657bb8cb831ae9","family_id":"qf-right-triangle-determination","seed":20260945,"semantic_template":"qf-right-triangle-determination/20260945"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 25°, 80°, 75°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0005","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"822c432230f07fb9a4e50d6e4b96e20b87346cd115df0ad4bac33ff62fccebed","family_id":"qf-right-triangle-determination","seed":20260946,"semantic_template":"qf-right-triangle-determination/20260946"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 30°, 90°, 60°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0006","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6dc3ef291f0ba72d002f39c4df48f0f4f9981fb01fa0db14331087f9ca9683b6","family_id":"qf-right-triangle-determination","seed":20260947,"semantic_template":"qf-right-triangle-determination/20260947"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 35°, 80°, 65°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0007","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9340a6ce14037954f0016bfe056318ea3198c3038fbf378a6143e99551f1acd7","family_id":"qf-right-triangle-determination","seed":20260948,"semantic_template":"qf-right-triangle-determination/20260948"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 40°, 90°, 50°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0008","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ed6dccac9f21dc60bd9ab6225d6c5f979c8566ff069c0236238be6845fea20a","family_id":"qf-right-triangle-determination","seed":20260949,"semantic_template":"qf-right-triangle-determination/20260949"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 45°, 80°, 55°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0009","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d6caf791c8ab57795439edf2cb1de2032034a9c603fed1ee4ded7bc647f770c","family_id":"qf-right-triangle-determination","seed":20260950,"semantic_template":"qf-right-triangle-determination/20260950"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 50°, 90°, 40°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0010","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7cc7911bfe8a690963eb1f4de3454ada7dfdbb355acd4092e9302df1175ad8b6","family_id":"qf-right-triangle-determination","seed":20260951,"semantic_template":"qf-right-triangle-determination/20260951"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 55°, 80°, 45°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0011","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d67eae7493a713893307c18f1aa6623c760f1ac85c8f43739396a5822283d6b","family_id":"qf-right-triangle-determination","seed":20260952,"semantic_template":"qf-right-triangle-determination/20260952"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 60°, 90°, 30°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0012","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0acf0783ca8060c9082f8539a0877cb4c7bcf5c78ec210858a1c1946355b14ab","family_id":"qf-right-triangle-determination","seed":20260953,"semantic_template":"qf-right-triangle-determination/20260953"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 65°, 80°, 35°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0013","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dca2c3f45a1ee5c33eee3e69ce1c7e41113029361542202a6783d9ce650ba035","family_id":"qf-right-triangle-determination","seed":20260954,"semantic_template":"qf-right-triangle-determination/20260954"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 70°, 90°, 20°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0014","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ac1f1f296e2f497092a90dc11c816c0ecc1c809f6baacc6dac0d0d46a3305a8","family_id":"qf-right-triangle-determination","seed":20260955,"semantic_template":"qf-right-triangle-determination/20260955"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 75°, 80°, 25°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0015","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df8099611d50fe79f19c33959f8ea69a6dfd6d582c694c75ba5a09ce6c652ed5","family_id":"qf-right-triangle-determination","seed":20260956,"semantic_template":"qf-right-triangle-determination/20260956"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 90°, 10°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0016","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa269d3cfd87313e0de144d9843bf329e7d264dea55b8db73995a2d5a356696e","family_id":"qf-right-triangle-determination","seed":20260957,"semantic_template":"qf-right-triangle-determination/20260957"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 11°, 89°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0017","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9cbdecd6b3acc06a145256f97b6d74cd42103aebcaf37469e3919b9d3c39b93b","family_id":"qf-right-triangle-determination","seed":20260958,"semantic_template":"qf-right-triangle-determination/20260958"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 15°, 75°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0018","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f38c69832909bea938070cfda8cbec898fe0a925f11774ddb2cade64ae2a9843","family_id":"qf-right-triangle-determination","seed":20260959,"semantic_template":"qf-right-triangle-determination/20260959"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 19°, 81°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0019","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1617fdef76a3f7b35eb0c827b7571dff307d615580a5637277a31944150e5f70","family_id":"qf-right-triangle-determination","seed":20260960,"semantic_template":"qf-right-triangle-determination/20260960"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 23°, 67°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0020","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04c8f7be412c51eda50c304928800e22a7beece67a412bb48a5dab3c6ac6184c","family_id":"qf-right-triangle-determination","seed":20260961,"semantic_template":"qf-right-triangle-determination/20260961"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 27°, 73°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0021","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5bf3eb01d028b8f5c68e937580c226a898fc6f12ac1790f068badd748ce9b19","family_id":"qf-right-triangle-determination","seed":20260962,"semantic_template":"qf-right-triangle-determination/20260962"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 31°, 59°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0022","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a5a5851da49b2af451664e803dd2a6740464b5647699fc063f1cdb2ac3d3f74","family_id":"qf-right-triangle-determination","seed":20260963,"semantic_template":"qf-right-triangle-determination/20260963"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 35°, 65°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0023","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2b6b665f8d7e26d2841ea93919688ddfc0aabe79417c35ad4dc865593f71a0d","family_id":"qf-right-triangle-determination","seed":20260964,"semantic_template":"qf-right-triangle-determination/20260964"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 39°, 51°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0024","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"926b58d3e30950601d7111c8a5dad8e50717985c0272f75b9b5dfb6a0d53d216","family_id":"qf-right-triangle-determination","seed":20260965,"semantic_template":"qf-right-triangle-determination/20260965"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 43°, 57°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0025","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b3191c09c0dd74b5f1088bb16c0f5b53d8c82078c023dcedf42045376782579a","family_id":"qf-right-triangle-determination","seed":20260966,"semantic_template":"qf-right-triangle-determination/20260966"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 47°, 43°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0026","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fb92d8c93e90a2fa027870f24a2457b6785b94152025f00ce447cb4c91945ca0","family_id":"qf-right-triangle-determination","seed":20260967,"semantic_template":"qf-right-triangle-determination/20260967"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 51°, 49°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0027","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de7f22ed6d17dcce557cf482c6bc2522607cd708b4faa1edc74df523021f4c46","family_id":"qf-right-triangle-determination","seed":20260968,"semantic_template":"qf-right-triangle-determination/20260968"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 55°, 35°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0028","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b6e08f222434aa68aa93356172b4e823a6834364fef71f14a24896fc1e1aa3f","family_id":"qf-right-triangle-determination","seed":20260969,"semantic_template":"qf-right-triangle-determination/20260969"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 59°, 41°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0029","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0283e660ccbb77015089b2376f48e0bd3270d017d6426de835938ed91ff0b8e","family_id":"qf-right-triangle-determination","seed":20260970,"semantic_template":"qf-right-triangle-determination/20260970"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 90°, 63°, 27°. Is it a right triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The angles sum to 180° and one angle is 90°, so the triangle is right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-right-triangle-determination-0030","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e4a2c65c13f0289d3ab2e4318941cb434643294dd5d515d89eb80ba11619172","family_id":"qf-right-triangle-determination","seed":20260971,"semantic_template":"qf-right-triangle-determination/20260971"},"fields":{"title":"Identifying a Right Triangle","stem":"A nondegenerate triangle has interior angles 80°, 67°, 33°. Is it a right triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"Although the angles sum to 180°, none is 90°, so the triangle is not right."},"skills":["interior-angle classification","triangle angle sum"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0001","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c137c43b3cabdad9b0f315380f68b39812eca3c25c1cf0bb1bae9e6be49d5c1","family_id":"qf-pythagorean-missing-side","seed":20260972,"semantic_template":"qf-pythagorean-missing-side/20260972"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 3 and 4. Find the hypotenuse length c.","answer":{"kind":"numeric","value":5,"explanation":"c=√(3²+4²)=5."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0002","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed816224ea2d01a033fbf999d5254dad1a9aeb17d1e02fd855cb34edbb6bfcc0","family_id":"qf-pythagorean-missing-side","seed":20260973,"semantic_template":"qf-pythagorean-missing-side/20260973"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 12 and a hypotenuse of length 13. Find the other leg length a.","answer":{"kind":"numeric","value":5,"explanation":"a=√(13²−12²)=5."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0003","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e068d606cd3480487e067b431f4ec3c0f6de588b33f441b2aa31844e56b75fe","family_id":"qf-pythagorean-missing-side","seed":20260974,"semantic_template":"qf-pythagorean-missing-side/20260974"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 8 and 15. Find the hypotenuse length c.","answer":{"kind":"numeric","value":17,"explanation":"c=√(8²+15²)=17."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0004","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"939e02175f7e0f53f88b14294a26205302ad5fb89fe016c41fd143b772716393","family_id":"qf-pythagorean-missing-side","seed":20260975,"semantic_template":"qf-pythagorean-missing-side/20260975"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 24 and a hypotenuse of length 25. Find the other leg length a.","answer":{"kind":"numeric","value":7,"explanation":"a=√(25²−24²)=7."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0005","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d665322efeb1f8ed067f4808544ac9b15976c7440b19ed448a2d996fc8ca3df","family_id":"qf-pythagorean-missing-side","seed":20260976,"semantic_template":"qf-pythagorean-missing-side/20260976"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 20 and 21. Find the hypotenuse length c.","answer":{"kind":"numeric","value":29,"explanation":"c=√(20²+21²)=29."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0006","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3837df51c2cc81f0538e6b437536633c6fb32410f3f41f6dd8b715f6c7ad93a5","family_id":"qf-pythagorean-missing-side","seed":20260977,"semantic_template":"qf-pythagorean-missing-side/20260977"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 40 and a hypotenuse of length 41. Find the other leg length a.","answer":{"kind":"numeric","value":9,"explanation":"a=√(41²−40²)=9."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0007","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36c7fbef2950dbab33c3e747896cc1f1b6edb00f7ef8b01236c18c2ecf87b5d4","family_id":"qf-pythagorean-missing-side","seed":20260978,"semantic_template":"qf-pythagorean-missing-side/20260978"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 12 and 35. Find the hypotenuse length c.","answer":{"kind":"numeric","value":37,"explanation":"c=√(12²+35²)=37."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0008","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe3664a8b0a020e5934abdf73ae8eafa74c864eaace5f49fb8b475ca9490c84c","family_id":"qf-pythagorean-missing-side","seed":20260979,"semantic_template":"qf-pythagorean-missing-side/20260979"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 60 and a hypotenuse of length 61. Find the other leg length a.","answer":{"kind":"numeric","value":11,"explanation":"a=√(61²−60²)=11."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0009","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0df81ce161a69ff50e6e5872636636c79c6ffc66928a26921d5c008649e827cc","family_id":"qf-pythagorean-missing-side","seed":20260980,"semantic_template":"qf-pythagorean-missing-side/20260980"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 28 and 45. Find the hypotenuse length c.","answer":{"kind":"numeric","value":53,"explanation":"c=√(28²+45²)=53."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0010","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63476dcfd734a4e6ffeb22efa345a6e8fd181fd564ddd268280e840729e1cbc8","family_id":"qf-pythagorean-missing-side","seed":20260981,"semantic_template":"qf-pythagorean-missing-side/20260981"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 56 and a hypotenuse of length 65. Find the other leg length a.","answer":{"kind":"numeric","value":33,"explanation":"a=√(65²−56²)=33."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0011","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"602d9ee888ee9e1d329992e9a1677388dd7daa39c62c36802bdcaa339c7e1cb0","family_id":"qf-pythagorean-missing-side","seed":20260982,"semantic_template":"qf-pythagorean-missing-side/20260982"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 16 and 63. Find the hypotenuse length c.","answer":{"kind":"numeric","value":65,"explanation":"c=√(16²+63²)=65."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0012","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec9706f10a0245a54a198c15d8c908fc45d91416d2b60ea055a5be6931f329d3","family_id":"qf-pythagorean-missing-side","seed":20260983,"semantic_template":"qf-pythagorean-missing-side/20260983"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 55 and a hypotenuse of length 73. Find the other leg length a.","answer":{"kind":"numeric","value":48,"explanation":"a=√(73²−55²)=48."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0013","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39c47914e584ccb839b1ee3cd89fd47cc355ff5047cda673af903e2fce24be38","family_id":"qf-pythagorean-missing-side","seed":20260984,"semantic_template":"qf-pythagorean-missing-side/20260984"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 13 and 84. Find the hypotenuse length c.","answer":{"kind":"numeric","value":85,"explanation":"c=√(13²+84²)=85."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0014","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"593f1b4197330890a87af44e17ab0323977b70d153b878488d7353926b95a75a","family_id":"qf-pythagorean-missing-side","seed":20260985,"semantic_template":"qf-pythagorean-missing-side/20260985"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 77 and a hypotenuse of length 85. Find the other leg length a.","answer":{"kind":"numeric","value":36,"explanation":"a=√(85²−77²)=36."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0015","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a9331418194aeea39b1027dc969596b4cfaf28d9f8c0fd5eccde12a3a99b011","family_id":"qf-pythagorean-missing-side","seed":20260986,"semantic_template":"qf-pythagorean-missing-side/20260986"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 39 and 80. Find the hypotenuse length c.","answer":{"kind":"numeric","value":89,"explanation":"c=√(39²+80²)=89."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0016","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8df5cb21dd6df00d633aeb3b5f68cdc475f5b7fce803c22da78d528824f7d0b","family_id":"qf-pythagorean-missing-side","seed":20260987,"semantic_template":"qf-pythagorean-missing-side/20260987"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 72 and a hypotenuse of length 97. Find the other leg length a.","answer":{"kind":"numeric","value":65,"explanation":"a=√(97²−72²)=65."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0017","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98f7ce9468d6ec9921bf99fbdaa8afb974c92445570639f7bf0b6c866d560680","family_id":"qf-pythagorean-missing-side","seed":20260988,"semantic_template":"qf-pythagorean-missing-side/20260988"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 20 and 99. Find the hypotenuse length c.","answer":{"kind":"numeric","value":101,"explanation":"c=√(20²+99²)=101."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0018","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39fd43b8edc42c4c921a0d8b1fb3ff1f1feb1bb06bea000a8daf6b6b925bc860","family_id":"qf-pythagorean-missing-side","seed":20260989,"semantic_template":"qf-pythagorean-missing-side/20260989"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 91 and a hypotenuse of length 109. Find the other leg length a.","answer":{"kind":"numeric","value":60,"explanation":"a=√(109²−91²)=60."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0019","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed258426b99ecf9f2c3054a0d1e3892cc8e184a2670729669d753b6502b175e2","family_id":"qf-pythagorean-missing-side","seed":20260990,"semantic_template":"qf-pythagorean-missing-side/20260990"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 15 and 112. Find the hypotenuse length c.","answer":{"kind":"numeric","value":113,"explanation":"c=√(15²+112²)=113."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0020","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d909292d86a4ea92d5969d3b43f3365d229419ec44d2c443562ccbd04461ccd4","family_id":"qf-pythagorean-missing-side","seed":20260991,"semantic_template":"qf-pythagorean-missing-side/20260991"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 117 and a hypotenuse of length 125. Find the other leg length a.","answer":{"kind":"numeric","value":44,"explanation":"a=√(125²−117²)=44."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0021","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"074471fbbc51e0f37a026eb38ce4ab8ecfb8a6582c38e4ab8d519e5f327566c3","family_id":"qf-pythagorean-missing-side","seed":20260992,"semantic_template":"qf-pythagorean-missing-side/20260992"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 6 and 8. Find the hypotenuse length c.","answer":{"kind":"numeric","value":10,"explanation":"c=√(6²+8²)=10."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0022","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a94567713810c32d2e35dedb369dc39d52263409f20b6de510b28ed6d3456204","family_id":"qf-pythagorean-missing-side","seed":20260993,"semantic_template":"qf-pythagorean-missing-side/20260993"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 24 and a hypotenuse of length 26. Find the other leg length a.","answer":{"kind":"numeric","value":10,"explanation":"a=√(26²−24²)=10."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0023","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5fcd14a90aef20026d113c956f904026424cd8a1a8a1905b72017ecf60702e80","family_id":"qf-pythagorean-missing-side","seed":20260994,"semantic_template":"qf-pythagorean-missing-side/20260994"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 16 and 30. Find the hypotenuse length c.","answer":{"kind":"numeric","value":34,"explanation":"c=√(16²+30²)=34."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0024","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81404f39c507387e0bcdef53a470f0a59c7e832e77d6684f24430f5022c0da47","family_id":"qf-pythagorean-missing-side","seed":20260995,"semantic_template":"qf-pythagorean-missing-side/20260995"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has one leg of length 48 and a hypotenuse of length 50. Find the other leg length a.","answer":{"kind":"numeric","value":14,"explanation":"a=√(50²−48²)=14."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-missing-side-0025","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18ffbd2d7f1e89287ca3f3b9242c4ba3410c980c35984fcb98775933a86fb210","family_id":"qf-pythagorean-missing-side","seed":20260996,"semantic_template":"qf-pythagorean-missing-side/20260996"},"fields":{"title":"Missing Side by the Pythagorean Theorem","stem":"A right triangle has leg lengths 40 and 42. Find the hypotenuse length c.","answer":{"kind":"numeric","value":58,"explanation":"c=√(40²+42²)=58."},"skills":["Pythagorean theorem","square roots"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0001","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"06809a825e94d636af6b739ac332e42e311f82b75dfbfe354bfbdfc66c656fea","family_id":"qf-pythagorean-counterexample","seed":20260997,"semantic_template":"qf-pythagorean-counterexample/20260997"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 3, 4, 7; B: 3, 4, 5; C: 3, 4, 5; D: 3, 4, 5","answer":{"kind":"choice","value":"A","choices":["A","B","C","D"],"explanation":"For option A, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0002","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53ab391f3b0da4928bf8718bcd8174dd33dacface9fca2b340c7b4109e4c9be2","family_id":"qf-pythagorean-counterexample","seed":20260998,"semantic_template":"qf-pythagorean-counterexample/20260998"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 5, 12, 13; B: 5, 13, 13; C: 5, 12, 13; D: 5, 12, 13","answer":{"kind":"choice","value":"B","choices":["A","B","C","D"],"explanation":"For option B, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0003","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffa9c5c95a90bb79a32d89caa401e6a02ddc28049934089c0de52f8211804485","family_id":"qf-pythagorean-counterexample","seed":20260999,"semantic_template":"qf-pythagorean-counterexample/20260999"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 8, 15, 17; B: 8, 15, 17; C: 10, 15, 17; D: 8, 15, 17","answer":{"kind":"choice","value":"C","choices":["A","B","C","D"],"explanation":"For option C, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0004","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85514e9f831263e0c994e93fe13d2de3faae9cca396de24a723900c38000a483","family_id":"qf-pythagorean-counterexample","seed":20261000,"semantic_template":"qf-pythagorean-counterexample/20261000"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 7, 24, 25; B: 7, 24, 25; C: 7, 24, 25; D: 7, 24, 27","answer":{"kind":"choice","value":"D","choices":["A","B","C","D"],"explanation":"For option D, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0005","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4686e3772ff1bac09b28681c83442b40bfcd50eb3e4c229395dcaba901bbb354","family_id":"qf-pythagorean-counterexample","seed":20261001,"semantic_template":"qf-pythagorean-counterexample/20261001"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 20, 22, 29; B: 20, 21, 29; C: 20, 21, 29; D: 20, 21, 29","answer":{"kind":"choice","value":"A","choices":["A","B","C","D"],"explanation":"For option A, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0006","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d5f9d9bbb2b1c768beea9ba2b1e5c88c48ae87e88093c7b601c979198eb6afb9","family_id":"qf-pythagorean-counterexample","seed":20261002,"semantic_template":"qf-pythagorean-counterexample/20261002"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 9, 40, 41; B: 11, 40, 41; C: 9, 40, 41; D: 9, 40, 41","answer":{"kind":"choice","value":"B","choices":["A","B","C","D"],"explanation":"For option B, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0007","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96f6e1da877157f8247799e967bb68f2d6b38e23a5b50ab5370c5c5d04887bf5","family_id":"qf-pythagorean-counterexample","seed":20261003,"semantic_template":"qf-pythagorean-counterexample/20261003"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 12, 35, 37; B: 12, 35, 37; C: 12, 35, 39; D: 12, 35, 37","answer":{"kind":"choice","value":"C","choices":["A","B","C","D"],"explanation":"For option C, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0008","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"635813d18b2c365aacce34292745696cea62a270fe78d6e70000745ca182a47d","family_id":"qf-pythagorean-counterexample","seed":20261004,"semantic_template":"qf-pythagorean-counterexample/20261004"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 11, 60, 61; B: 11, 60, 61; C: 11, 60, 61; D: 11, 61, 61","answer":{"kind":"choice","value":"D","choices":["A","B","C","D"],"explanation":"For option D, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0009","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a49a475fd00a46be4ded6b3d73125a0b70f75b76168e4587727bbcd83f8d2fa","family_id":"qf-pythagorean-counterexample","seed":20261005,"semantic_template":"qf-pythagorean-counterexample/20261005"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 30, 45, 53; B: 28, 45, 53; C: 28, 45, 53; D: 28, 45, 53","answer":{"kind":"choice","value":"A","choices":["A","B","C","D"],"explanation":"For option A, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0010","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd79865b99fb458158d704b84bb0b5a4c10ec8e7a4e4c78e32db5b65f218b4ad","family_id":"qf-pythagorean-counterexample","seed":20261006,"semantic_template":"qf-pythagorean-counterexample/20261006"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 33, 56, 65; B: 33, 56, 67; C: 33, 56, 65; D: 33, 56, 65","answer":{"kind":"choice","value":"B","choices":["A","B","C","D"],"explanation":"For option B, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0011","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"934152a73b2136f4dc13fbb8af9c19e3363dc24d41034e020b1e54c6fb8c07ad","family_id":"qf-pythagorean-counterexample","seed":20261007,"semantic_template":"qf-pythagorean-counterexample/20261007"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 16, 63, 65; B: 16, 63, 65; C: 16, 64, 65; D: 16, 63, 65","answer":{"kind":"choice","value":"C","choices":["A","B","C","D"],"explanation":"For option C, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0012","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2105e713d387cd2fd182a34707ab3d2487f5b427c4041dbfd3d5f547e778b348","family_id":"qf-pythagorean-counterexample","seed":20261008,"semantic_template":"qf-pythagorean-counterexample/20261008"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 48, 55, 73; B: 48, 55, 73; C: 48, 55, 73; D: 50, 55, 73","answer":{"kind":"choice","value":"D","choices":["A","B","C","D"],"explanation":"For option D, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0013","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"793cbd429c8a32e0c4a20accc34ec016eefa6c02286344f745442b9d0b0dcd1c","family_id":"qf-pythagorean-counterexample","seed":20261009,"semantic_template":"qf-pythagorean-counterexample/20261009"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 13, 84, 87; B: 13, 84, 85; C: 13, 84, 85; D: 13, 84, 85","answer":{"kind":"choice","value":"A","choices":["A","B","C","D"],"explanation":"For option A, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0014","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b20de6ca1371ef570bd7a54d5dfca03483f173a3c9d3af90bb4b826a2c3dbc0","family_id":"qf-pythagorean-counterexample","seed":20261010,"semantic_template":"qf-pythagorean-counterexample/20261010"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 36, 77, 85; B: 36, 78, 85; C: 36, 77, 85; D: 36, 77, 85","answer":{"kind":"choice","value":"B","choices":["A","B","C","D"],"explanation":"For option B, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260912-pythagorean-counterexample-0015","batch_id":"batch-20260912-geometry-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29c824714a25900fea4f597ab8e8af440167582fbf81ee7d22e4b7ff11937dd3","family_id":"qf-pythagorean-counterexample","seed":20261011,"semantic_template":"qf-pythagorean-counterexample/20261011"},"fields":{"title":"Counterexample to the Pythagorean Relation","stem":"Which positive triple does not satisfy a²+b²=c², taking the last number in each triple as c?\nA: 39, 80, 89; B: 39, 80, 89; C: 41, 80, 89; D: 39, 80, 89","answer":{"kind":"choice","value":"C","choices":["A","B","C","D"],"explanation":"For option C, a²+b² is not equal to c², so it is the counterexample to the stated squared relation."},"skills":["squared relation","counterexample identification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}