Problem

Source: Iran second round 2011

Tags: linear algebra, matrix, trigonometry, geometry, angle bisector, geometry proposed



In triangle $ABC$, we have $\angle ABC=60$. The line through $B$ perpendicular to side $AB$ intersects angle bisector of $\angle BAC$ in $D$ and the line through $C$ perpendicular $BC$ intersects angle bisector of $\angle ABC$ in $E$. prove that $\angle BED\le 30$.