Question 90
Let $AB$ be the longest side of the triangle $ABC$. Let $M$ and $N$ denote the points on the side $AB$, such that $|AM| = |AC|$ and $|BN| = |BC|$. Denote the midpoints of the segments $MC$ and $NC$ by $P$ and $R$. The incircle of the triangle $ABC$ touches the sides $BC$ and $AC$ at $D$ and $E$. Prove that the points $P, R, D$ and $E$ are concyclic.