CWMO 2001 Problem 6

$P$ is a point on the exterior of a circle centered at $O$ . The tangents to the circle from $P$ touch the circle at $A$ and $B$ . Let $Q$ be the point of intersection of $PO$ and $AB$ . Let $CD$ be any chord of the circle passing through $Q$ . Prove that $\triangle PAB$ and $\triangle PCD$ have the same incentre.