MathNet 2023-part-07 — 187 problems (EN–VI) Question 77

Triangle $ABC$ with $\angle BAC \gt 90^{\circ}$ has $AB = 5$ and $AC = 7$. Points $D$ and $E$ lie on segment $BC$ such that $BD = DE = EC$. If $\angle BAC + \angle DAE = 180^{\circ}$, compute $BC$.