MathNet 2008-part-03 — 165 problems (EN–VI) Question 57

In the triangle $ABC$, $\angle BAC = 120^\circ$. On the bisector of the angle $\angle BAC$, a point $D$ is chosen such that $\overline{AD} = \overline{AB} + \overline{AC}$. Prove that $\triangle BCD$ is equilateral.