CH-SMO 2010 Problem 2

Let $\triangle{ABC}$ be a triangle with $AB\not=AC$ . The incircle with centre $I$ touches $BC$ , $CA$ , $AB$ at $D$ , $E$ , $F$ , respectively. Furthermore let $M$ the midpoint of $EF$ and $AD$ intersect the incircle at $P\not=D$ . Show that $PMID$ ist cyclic.