RO-TST 2013 Problem 2

Circles $\Omega$ and $\omega$ are tangent at a point $P$ ( $\omega$ lies inside $\Omega$ ). A chord $AB$ of $\Omega$ is tangent to $\omega$ at $C;$ the line $PC$ meets $\Omega$ again at $Q.$ Chords $QR$ and $QS$ of $\Omega$ are tangent to $\omega .$ Let $I,X,$ and $Y$ be the incenters of the triangles $APB,$ $ARB,$ and $ASB,$ respectively. Prove that $\angle PXI+\angle PYI=90^{\circ }.$