KMO 2008 Problem 5

Quadrilateral $ABCD$ is inscribed in a circle $O$ . Let $AB\cap CD=E$ and $P\in BC, EP\perp BC$ , $R\in AD, ER\perp AD$ , $EP\cap AD=Q, ER\cap BC=S$ Let $K$ be the midpoint of $QS$ Prove that $E, K, O$ are collinear.