Question 154
Given triangle $A B C$ inscribed in $(O)$. Two tangents at $B$, $C$ of $(O)$ intersect at $P$. The bisector of angle $A$ intersects $(P, P B)$ (the circle with center $P$ and radius $P B$) at point $E$ lying inside triangle $A B C$. Let $M$, $N$ be the midpoints of two arcs $B C$ of $(O)$ such that $M$ and $A$ are on different sides of $B C$. The circle with diameter $B C$ intersects the line segment $E N$ at $F$. Prove that the orthocenter of triangle $E F M$ belongs to $B C$.