RMO 2013 D5

In a triangle $ABC$ , let $H$ denote its orthocentre. Let $P$ be the reflection of $A$ with respect to $BC$ . The circumcircle of triangle $ABP$ intersects the line $BH$ again at $Q$ , and the circumcircle of triangle $ACP$ intersects the line $CH$ again at $R$ . Prove that $H$ is the incentre of triangle $PQR$ .