# Concept derivation guides

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Concept guide



## [Circle: classifying points as inside, on or outside by squared distance, including radius zero](/en/derivations/derivation-mko-circle-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-circle)

In an equal-unit orthonormal frame take center O=(2,−1) and radius r=5. Decide whether each of A=(5,3), B=(4,1), E=(−2,3) is strictly inside, on, or outside the circle; verify that the four axial points O±(5,0), O±(0,5) lie on C(O,5), and compute from two opposite axial points the diameter length 2r=10. Then change the radius to r=0, prove that C(O,0)={O} and that no point is strictly inside, and classify B.

Circle boundaries and zero-radius degeneracy

derivation-mko-circle-01





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