Question 54
Let $PQ$ be the diameter of semicircle $H$. Circle $\omega$ 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 $AB$ is perpendicular to $PQ$ and tangent to $\omega$. Prove that $AC$ bisects $\angle PAB$.