CN-SMO 2007 Problem 2

$AB$ is the diameter of semicircle $O$ . $C$ , $D$ are two arbitrary points on semicircle $O$ . Point $P$ lies on line $CD$ such that line $PB$ is tangent to semicircle $O$ at $B$ . Line $PO$ intersects line $CA$ , $AD$ at point $E$ , $F$ respectively. Prove that $OE$ = $OF$ .