OMM 2004 Problem 3

Let $Z$ and $Y$ be the tangency points of the incircle of the triangle $ABC$ with the sides $AB$ and $CA$ , respectively. The parallel line to $Y Z$ through the midpoint $M$ of $BC$ , meets $CA$ in $N$ . Let $L$ be the point in $CA$ such that $NL = AB$ (and $L$ on the same side of $N$ than $A$ ). The line $ML$ meets $AB$ in $K$ . Prove that $KA = NC$ .