SMO 2017 Problem 1

The incircle of $\vartriangle ABC$ touches the sides $BC,CA,AB$ at $D,E,F$ respectively. A circle through $A$ and $B$ encloses $\vartriangle ABC$ and intersects the line $DE$ at points $P$ and $Q$ . Prove that the midpoint of $AB$ lies on the circumircle of $\vartriangle PQF$ .