PL-OM 2018 Problem 5

An acute triangle $ABC$ in which $AB<AC$ is given. Points $E$ and $F$ are feet of its heights from $B$ and $C$ , respectively. The line tangent in point $A$ to the circle escribed on $ABC$ crosses $BC$ at $P$ . The line parallel to $BC$ that goes through point $A$ crosses $EF$ at $Q$ . Prove $PQ$ is perpendicular to the median from $A$ of triangle $ABC$ .