Question 26
The incircle of $\triangle ABC$ touches the sides $BC$, $CA$, $AB$, at $D$, $E$, $F$ respectively. A circle through $A$ and $B$ encloses $\triangle ABC$ and intersects the line $DE$ at points $P$ and $Q$. Prove that the midpoint of $AB$ lies on the circumcircle of $\triangle PQF$.