Let $AL$ and $BK$ be the angle bisectors in the non-isosceles triangle $ABC$ ($L$ lies on the side $BC$, $K$ lies on the side $AC$). The perpendicular bisector of $BK$ intersects line $AL$ at $M$. The point $N$ is on the line $BK$ such that $LN$ is parallel to $MK$. Prove that $LN = NA$.
I am at a complete loss here, the hint says that I must first prove that $AKMB$ is a cyclic quadrilateral but I've no idea how to prove it or what to do once I have.