IMO 2005-P1

Six points are chosen on the sides of an equilateral triangle ABC: A1, A2 on BC, B1, B2 on CA and C1, C2 on AB, such that they are the vertices of a convex hexagon A1A2B1B2C1C2 with equal side lengths. Prove that the lines A1B2;B1C2 and C1A2 are concurrent.

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