OIM 1990 Problem 2

Let $ABC$ be a triangle. $I$ is the incenter, and the incircle is tangent to $BC$ , $CA$ , $AB$ at $D$ , $E$ , $F$ , respectively. $P$ is the second point of intersection of $AD$ and the incircle. If $M$ is the midpoint of $EF$ , show that $P$ , $I$ , $M$ , $D$ are concyclic.