Question 71
Given triangle $ABC$, let $AL$ be the angle bisector of $\angle BAC$ with $L$ on $BC$. Let the incircle of $\triangle ABC$ touch the sides $AB$ and $BC$ at points $P$ and $Q$ respectively. Let $X$ be the intersection point of the lines $AQ$ and $LP$. Show that the lines $BX$ and $AL$ are perpendicular.