MathNet 2017-part-02 — 176 problems (EN–VI) Question 52

Let $ABC$ be an acute triangle with orthocenter $H$. The bisector of angle $BHC$ intersects side $BC$ at $D$. Denote by $E$, $F$ the reflections of $D$ about $AB$, $AC$, respectively. Prove that the circumcircle of triangle $AEF$ passes through the midpoint of arc $BAC$.

(Patrik Bak)