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MathNet 2010 — Part 04 Question 24

Math Olympiad Vault · MathNet 2010 — Part 04

Question 24

The point $O$ is the centre of the circumcircle of triangle $\Delta ABC$.
The line $AO$ intersects the side $BC$ in point $N$, and the line $BO$ the side $AC$ in point $M$. Prove that, if $CM = CN$, then $AC = BC$.