Olympiad Geometry · Challenge problem

Equilateral triangles $ABD$ and $ACE$ are drawn outside $\triangle ABC$, on sides $\overline{AB}$ and $\overline{AC}$. Segments $\overline{BE}$ and $\overline{CD}$ meet at $O$. If $m\angle BAC = 50^\circ$, find $m\angle BOC$.