IL-GILLIS 1995 Problem 2

Let $PQ$ be the diameter of semicircle $H$ . Circle $O$ is internally tangent to $H$ and tangent to $PQ$ at $C$ . Let $A$ be a point on $H$ and $B$ a point on $PQ$ such that $AB\perp PQ$ and is tangent to $O$ . Prove that $AC$ bisects $\angle PAB$