KMO 2013 Problem 1

Let $P$ be a point on segment $BC$ . $Q, R$ are points on $AC, AB$ such that $PQ \parallel AB$ and $PR \parallel AC$ . $O, O_{1}, O_{2}$ are the circumcenters of triangle $ABC, BPR, PCQ$ . The circumcircles of $BPR, PCQ$ meet at point $K (\ne P)$ . Prove that $OO_{1} = KO_{2}$ .