Let $S$ be an incenter of triangle $ABC$ and let incircle touch sides $AC$ and $AB$ in points $P$ and $Q$, respectively. Lines $BS$ and $CS$ intersect line $PQ$ in points $M$ and $N$, respectively. Prove that points $M$, $N$, $B$ and $C$ are concyclic
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012
Tags: geometry, incenter, incircle