OBM 2022 Problem 2

Let $ABC$ be an acute triangle, with $AB<AC$ . Let $K$ be the midpoint of the arch $BC$ that does not contain $A$ and let $P$ be the midpoint of $BC$ . Let $I_B,I_C$ be the $B$ -excenter and $C$ -excenter of $ABC$ , respectively. Let $Q$ be the reflection of $K$ with respect to $A$ . Prove that the points $P,Q,I_B,I_C$ are concyclic.