Question 93
Suppose that $A_1A_2A_3A_4A_5$ is a convex pentagon in the cartesian plane with all its vertices having rational coordinates. For each $1 \le i \le 5$, define $B_i$ as the intersection point of the extensions of the sides $A_{i+1}A_{i+2}$ and $A_{i+3}A_{i+4}$ (the vertices of the pentagon are numbered in a cyclic manner, i.e for each $1 \le i \le 5$, $A_i = A_{i+5}$). Prove that at most three of the lines $A_iB_i$, $1 \le i \le 5$, are concurrent.