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Triangle and two angles

Source: Sharygin contest. The final raund. 2008. Grade 8. First day. Problem 4

August 31, 2008
symmetrygeometryparallelogramangle bisectorgeometry unsolved

Problem Statement

(F.Nilov, A.Zaslavsky) Let CC0 CC_0 be a median of triangle ABC ABC; the perpendicular bisectors to AC AC and BC BC intersect CC0 CC_0 in points A′ A', B′ B'; C1 C_1 is the meet of lines AA′ AA' and BB′ BB'. Prove that \angle C_1CA \equal{} \angle C_0CB.
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