VTMO 2026 - Grade 9 - Semifinal - SET 05 - Self-study Question 12

In the figure, triangle $ABC$ is isosceles with $AB=AC$. Equilateral triangle $DEF$ lies inside it, with $D\in AB,E\in BC,F\in AC$. Given $\angle ADF=50^\circ$ and $\angle A=\frac12\angle DEF$, find $\angle BED$.