MathNet 2006 — Part 02 Question 61

Given a triangle $ABC$, let $BL$, $L \in AC$, be the bisector of $\angle ABC$ and $AH$, $H \in BC$, the altitude to $BC$. Prove that $\angle AHL = \angle ALB$ if and only if $\angle BAC = \angle ACB + 90^\circ$.