Question 96
The in-circle of triangle $ABC$ touches the sides $BC$, $CA$ and $AB$ in $K$, $L$ and $M$ respectively. The line through $A$ and parallel to $LK$ meets $MK$ in $P$ and the line through $A$ and parallel to $MK$ meets $LK$ in $Q$. Show that the line $PQ$ bisects the sides $AB$ and $AC$ of triangle $ABC$.