Τρίτη, 17 Οκτωβρίου 2017

2005 IMO Shortlist G2

Six points are chosen on the sides of an equilateral triangle $ABC$: $A_1, A_2$ on $BC, B_1, B_2$ on $CA$, and $C_1, C_2$ on $AB$, so that they are the vertices of a convex hexagon $A_1A_2B_1B_2C_1C_2$ with equal side lengths. Prove that the lines $A_1B_2, B_1C_2$  and $C_1A_2$  are concurrent.

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