Question 70
Let $H$ be the orthocenter of an acute triangle $ABC$. The circumcircle of $ABC$ and the circle with a diameter $[AH]$ meet at a point $E$ which is different from $A$. Let $M$ be the midpoint of the smaller arc $BC$ of circumcircle of triangle $ABC$, and $N$ be the midpoint of the greater arc $BC$ of circumcircle of triangle $BHC$. Prove that the points $E$, $H$, $M$, $N$ are concyclic.