In acute $\Delta ABC$, $O$ is circumcentre. $M,N$ on $AB,AC$, s.t. $O$ lies on $MN$. $D,E,F$ are midpoints of $MN,BN,CM$. Prove O,D,E,F are concyclic.

score 69 · Answer 15 · 2026-04-11 12:15:18

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Triangle-formation given three unique line segments with integer lengths ranging from 1 to 100. Probability?

Published on 11 Apr 2026 - 12:15

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In acute $\Delta ABC$, $O$ is circumcentre. $M,N$ on $AB,AC$, s.t. $O$ lies on $MN$. $D,E,F$ are midpoints of $MN,BN,CM$. Prove O,D,E,F are concyclic.

Triangle-formation given three unique line segments with integer lengths ranging from 1 to 100. Probability?

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