Question 101
On the extensions of the sides $CA$ and $AB$ of triangle $ABC$ beyond points $A$ and $B$, points $E$ and $F$ are chosen such that $AE = BC$ and $BF = AC$. The $A$-excircle is tangent to segment $BF$ at point $N$. Let $M$ be the midpoint of segment $EF$. Prove that $MN$ is parallel to the internal angle bisector of angle $A$.