PMO 2017 Problem 4

Circles $\mathcal{C}_1$ and $\mathcal{C}_2$ with centers at $C_1$ and $C_2$ respectively, intersect at two points $A$ and $B$. Points $P$ and $Q$ are varying points on $\mathcal{C}_1$ and $\mathcal{C}_2$, respectively, such that $P$, $Q$ and $B$ are collinear and $B$ is always between $P$ and $Q$. Let lines $PC_1$ and $QC_2$ intersect at $R$, let $I$ be the incenter of $\Delta PQR$, and let $S$ be the circumcenter of $\Delta PIQ$. Show that as $P$ and $Q$ vary, $S$ traces the arc of a circle whose center is concyclic with $A$, $C_1$ and $C_2$.