KöMaL 2014 B4627

The angle bisector drawn from right-angled vertex $C$ of triangle $ABC$ intersects the circumscribed circle at point $P$ , and the angle bisector from vertex $A$ intersects the circumscribed circle at point $Q$ . $K$ is the intersection of line segments $PQ$ and $AB$ . The centre of the inscribed circle is $O$ , and its point of tangency on side $AC$ is $E$ . Prove that points $E$ , $O$ and $K$ are collinear.