Question 169
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 $AB$. These points are the vertices of a convex hexagon $A_1A_2B_1B_2C_1C_2$ with sides of equal length. Prove that the lines $A_1B_2$, $B_1C_2$ and $C_1A_2$ are concurrent. (proposed by Romania, average score 2.61.)