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Collinear (diagonal intersect perp bisector)'s in a heaxgon

Source: XVIII Tuymaada Mathematical Olympiad (2011), Senior Level

July 29, 2011
geometryperpendicular bisectorgeometry unsolved

Problem Statement

In a convex hexagon AC′BA′CB′AC'BA'CB', every two opposite sides are equal. Let A1A_1 denote the point of intersection of BCBC with the perpendicular bisector of AA′AA'. Define B1B_1 and C1C_1 similarly. Prove that A1A_1, B1B_1, and C1C_1 are collinear.
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