IR-MO 2002 Problem 24

$A,B,C$ are on circle $\mathcal C$ . $I$ is incenter of $ABC$ , $D$ is midpoint of arc $BAC$ . $W$ is a circle that is tangent to $AB$ and $AC$ and tangent to $\mathcal C$ at $P$ . ( $W$ is in $\mathcal C$ ) Prove that $P$ and $I$ and $D$ are on a line.