Question 26
In triangle $ABC$ we have $\angle BAC = 60^\circ$. The perpendicular line to $AB$ at $B$ intersects the bisector of $\angle BAC$ at $D$ and the perpendicular line to $BC$ at $C$ meets the bisector of $\angle ABC$ at $E$. Prove that $\angle BED \leq 30^\circ$.