Question 33
Let $ABC$ be a triangle inscribed in a circle $\Gamma$. Let $\Gamma_a$ be a circle tangent internally to $\Gamma$ and to the sides $AB$ and $AC$. Let $A'$ be the point of tangency of $\Gamma$ and $\Gamma_a$. Define $B'$ and $C'$ similarly. Prove that $AA'$, $BB'$, and $CC'$ are concurrent.