MathNet 2009-part-02 — 175 problems (EN–VI) Question 132

Let $M$ be the circumcenter of triangle $ABC$. $C_1, A_1, B_1$ the circumcenters of triangles $ABM, BCM, CAM$ respectively. Prove that, the lines $AA_1, BB_1, CC_1$ intersect in same point.

(proposed by M. Batbileg)