KöMaL 2012 B4490

$P$ and $Q$ are interior points on side $AC$ of a non-isosceles triangle ABC such that $\angle ABP = \angle QBC< \frac 12\cdot \angle ABC$ . The interior angle bisectors drawn from $A$ and $C$ intersect the line segment $BP$ at points $K$and $L$, and the line segment $BQ$ at points $M$ and $N$, respectively. Prove that the lines $AC$, $KN$ and $LM$ are concurrent.