PAMO 2016 Problem 1

Two circles $\mathcal{C}_1$ and $\mathcal{C}_2$ intersect each other at two distinct points $M$ and $N$ . A common tangent lines touches $\mathcal{C}_1$ at $P$ and $\mathcal{C}_2$ at $Q$ , the line being closer to $N$ than to $M$ . The line $PN$ meets the circle $\mathcal{C}_2$ again at the point $R$ . Prove that the line $MQ$ is a bisector of the angle $\angle{PMR}$ .