IrMO 2013 Problem 5

$A, B$ and $C$ are points on the circumference of a circle with centre $O$ . Tangents are drawn to the circumcircles of triangles $OAB$ and $OAC$ at $P$ and $Q$ respectively, where $P$ and $Q$ are diametrically opposite $O$ . The two tangents intersect at $K$ . The line $CA$ meets the circumcircle of $\triangle OAB$ at $A$ and $X$ . Prove that $X$ lies on the line $KO$ .