Question 79
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 again $\Omega$ at $Q$. Chords $QR$ and $QS$ of $\Omega$ are tangent to $\omega$. Let $I, X$, and $Y$ be the incentres of the triangles $APB, ARB$, and $ASB$, respectively. Prove that
$$
\angle PXI + \angle PYI = 90^{\circ}.
$$
$$
\angle PXI + \angle PYI = 90^{\circ}.
$$