MathNet 2019-part-01 — 184 problems (EN–VI) Question 3

In triangle $ABC$, let $D$ and $E$ be points on the sides $AB$ and $AC$ respectively such that $BD = CE$. Let $M$ and $N$ be the midpoints of $BC$ and $DE$ respectively.
Prove that the bisector of angle $BAC$ is parallel to the line $MN$.