Let $\Gamma$ be the incircle of a non-isosceles triangle $ABC$, $I$ be it’s incenter. Let $A_1, B_1, C_1$ be the tangency points of $\Gamma$ with the sides $BC, AC, AB$ respectively. Let $A_2 = \Gamma \cap AA_1$, $M = C_1B_1 \cap AI$, $P$ and $Q$ be the other (different from $A_1$ and $A_2$) intersection points of $\Gamma$ and $A_1M$, $A_2M$ respectively. Prove that $A$, $P$ and $Q$ are colinear.