IR-MO 2013 Problem 8

Let $A_1A_2A_3A_4A_5$ be a convex 5-gon in which the coordinates of all of it's vertices are rational. For each $1\leq i \leq 5$ define $B_i$ the intersection of lines $A_{i+1}A_{i+2}$ and $A_{i+3}A_{i+4}$ . ( $A_i=A_{i+5}$ ) Prove that at most 3 lines from the lines $A_iB_i$ ( $1\leq i \leq 5$ ) are concurrent.

Time allowed for this problem was 75 minutes.