The inscribed circle of $\Delta ABC$ $(AC<BC)$ is tangent to $AC$ and $BC$ in points $X$ and $Y$ respectively. A line is constructed through the middle point $M$ of $AB$, parallel to $XY$, which intersects $BC$ in $N$. Let $L\in BC$ be such that $NL=AC$ and $L$ is between $C$ and $N$. The lines $ML$ and $AC$ intersect in point $K$. Prove that $BN=CK$.
Problem
Source: II International Festival of Young Mathematicians Sozopol 2011, Theme for 10-12 grade
Tags: geometry, Menelaus