Question 64
Let $AB$ be a chord of circle $\Gamma$. Let $O$ be the centre of a circle which is tangent to $AB$ at $C$ and internally tangent to $\Gamma$ at $P$. Point $C$ lies between $A$ and $B$. Let the circumcircle of triangle $POC$ intersect $\Gamma$ at distinct points $P$ and $Q$. Prove that $\angle AQP = \angle CQB$.