KMO 2014 Problem 3

$AB$ is a chord of $O$ and $AB$ is not a diameter of $O$ . The tangent lines to $O$ at $A$ and $B$ meet at $C$ . Let $M$ and $N$ be the midpoint of the segments $AC$ and $BC$ , respectively. A circle passing through $C$ and tangent to $O$ meets line $MN$ at $P$ and $Q$ . Prove that $\angle PCQ = \angle CAB$ .