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 $A_2{B}_3$ and $B_2{A}_3$. \par Let $C_2$ be the intersection of the lines $A_3{B}_1$ and $B_3{A}_1$. \par Let $C_3$ be the intersection of the lines $A_1{B}_2$ and $B_1{A}_2$. \par Then $C_1,C_2$ and $C_3$ are collinear.

Return to puzzle page.