KMO 2013 Problem 6

Let $O$ be circumcenter of triangle $ABC$ . For a point $P$ on segmet $BC$ , the circle passing through $P, B$ and tangent to line $AB$ and the circle passing through $P, C$ and tangent to line $AC$ meet at point $Q ( \ne P )$ . Let $D, E$ be foot of perpendicular from $Q$ to $AB, AC$ . ( $D \ne B, E \ne C$ ) Two lines $DE$ and $BC$ meet at point $R$ . Prove that $O, P, Q$ are collinear if and only if $A, R, Q$ are collinear.