SILK-ROAD 2003 Problem 2

Let $s=\frac{AB+BC+AC}{2}$ be half-perimeter of triangle $ABC$ . Let $L$ and $N$ be a point's on ray's $AB$ and $CB$ , for which $AL=CN=s$ . Let $K$ is point, symmetric of point $B$ by circumcenter of $ABC$ . Prove, that perpendicular from $K$ to $NL$ passes through incenter of $ABC$ .

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