PL-OM 2005 Problem 2

The points $A, B, C, D$ lie in this order on a circle $o$ . The point $S$ lies inside $o$ and has properties $\angle SAD=\angle SCB$ and $\angle SDA= \angle SBC$ . Line which in which angle bisector of $\angle ASB$ in included cut the circle in points $P$ and $Q$ . Prove $PS =QS$ .