SILK-ROAD 2002 Problem 1

Let $\triangle ABC$ be a triangle with incircle $\omega(I,r)$ and circumcircle $\zeta(O,R)$ .Let $l_{a}$ be the angle bisector of $\angle BAC$ .Denote $P=l_{a}\cap\zeta$ .Let $D$ be the point of tangency $\omega$ with $[BC]$ .Denote $Q=PD\cap\zeta$ .Show that $PI=QI$ if $PD=r$ .