Question 131
Let $ABC$ be an acute triangle with $AB\gt AC$. Let $F$ be the foot of the altitude from $A$ and $H$ the orthocenter. Choose $D$ on ray $BC$ beyond $C$. The circumcircle of $DFH$ meets segment $AD$ at a point $N$ which also lies on the circumcircle of $ABC$. Prove that $NH$ passes through the midpoint of $BC$.