MathNet 2017-part-04 — 176 problems (EN–VI) Question 7

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