OMCPLP 2020 Problem 4

Let $ABC$ be an acute triangle. Its incircle touches the sides $BC$ , $CA$ and $AB$ at the points $D$ , $E$ and $F$ , respectively. Let $P$ , $Q$ and $R$ be the circumcenters of triangles $AEF$ , $BDF$ and $CDE$ , respectively. Prove that triangles $ABC$ and $PQR$ are similar.