IR-MO 2002 Problem 21

Excircle of triangle $ABC$ corresponding vertex $A$ , is tangent to $BC$ at $P$ . $AP$ intersects circumcircle of $ABC$ at $D$ . Prove $$r(PCD)=r(PBD)$$ whcih $r(PCD)$ and $r(PBD)$ are inradii of triangles $PCD$ and $PBD$ .