BG-MO 2008 Problem 1

Let $ABC$ be an acute triangle and $CL$ be the angle bisector of $\angle ACB$ . The point $P$ lies on the segment $CL$ such that $\angle APB=\pi-\frac{_1}{^2}\angle ACB$ . Let $k_1$ and $k_2$ be the circumcircles of the triangles $APC$ and $BPC$ . $BP\cap k_1=Q, AP\cap k_2=R$ . The tangents to $k_1$ at $Q$ and $k_2$ at $B$ intersect at $S$ and the tangents to $k_1$ at $A$ and $k_2$ at $R$ intersect at $T$ . Prove that $AS=BT.$