Question 38
Let $\Gamma$ be the incircle of a none-isosceles triangle $ABC$, $I$ be its center. 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 $A_1$, $A_2$) intersection points of $A_1M$, $A_2M$ and $\Gamma$, respectively.
Prove that $A$, $P$, $Q$ are collinear.
Prove that $A$, $P$, $Q$ are collinear.