January 2001
Let $A_1, A_2, A_3, B_1, B_2, B_3 $ be six distinct points on the plane. \par $ A_1, A_2 $ and $ A_3 $ are collinear, likewise $ B_1, B_2 $ and $ B_3 $. \par Let $ C_1 $ be the intersection of the lines $ A_2B_3 $ and $ B_2A_3 $. \par Let $ C_2 $ be the intersection of the lines $ A_3B_1 $ and $ B_3A_1 $. \par Let $ C_3 $ be the intersection of the lines $ A_1B_2 $ and $ B_1A_2 $. \par Then $ C_1, C_2 $ and $ C_3 $ are collinear.
