Suppose $A_1,A_2,A_3,B_1,B_2,B_3$ are points in the plane such that for each $i,j\in\{1,2,3\}$ it holds that $A_iB_j=i+j$. What can be said about these six points?
Source: French MO 1995 P4
Tags: geometry
Suppose $A_1,A_2,A_3,B_1,B_2,B_3$ are points in the plane such that for each $i,j\in\{1,2,3\}$ it holds that $A_iB_j=i+j$. What can be said about these six points?