Question 16
Acute triangle $ABC$ with $AB \lt AC$ lies on $\left(O\right)$. Tangents at $B , C$ meet $M$; $MA$ meets $\left(O\right)$ again at $E$. The line through $E$ parallel to $BC$ meets $\left(O\right)$ again at $F$. Circle $\left(I\right)$ passes through $A$ and is tangent to $BC$ at $C$; it meets $AF$ again at $N$. Prove $BC$ is the perpendicular bisector of $NE$.