AMO 2017 Problem 2

Let $ABCDE$ be a regular pentagon with center $M$ . A point $P\neq M$ is chosen on the line segment $MD$ . The circumcircle of $ABP$ intersects the line segment $AE$ in $A$ and $Q$ and the line through $P$ perpendicular to $CD$ in $P$ and $R$ . Prove that $AR$ and $QR$ are of the same length.