Question 44
$I$ is the incenter of the triangle $ABC$ and the incircle touches $BC$, $CA$, $AB$ at $D$, $E$, $F$ respectively. $AD$ meets the incircle again at $P$. $M$ is the midpoint of $EF$. Show that $P$, $M$, $I$, $D$ are cyclic (or the points are collinear).