Question 15
Six points are chosen on the sides of an equilateral triangle ABC: $ A_1, A_2 $ on BC; $ B_1, B_2 $ on CA; $ C_1, C_2 $ on AB. These points are 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.