Question 59
Let $AB$ be the longest side of triangle $ABC$. Choose points $M,N$ on $AB$ such that $|AM|=|AC|$ and $|BN|=|BC|$. Let $P,R$ be the midpoints of $MC,NC$, respectively, and let the incircle of $ABC$ touch $BC,AC$ at $D,E$. Prove that $P,R,D,E$ are concyclic.