Question 119
Let $s = (AB + BC + AC)/2$ be the semiperimeter of triangle $ABC$. We choose two points $L$ and $N$ lying on the rays $AB$ and $CB$ satisfying $AL = CN = s$. Let $K$ be the point symmetric to $B$ with respect to the center of the circumcircle of triangle $ABC$. Prove that the perpendicular drawn from the point $K$ to the line $NL$ passes through the incenter of the triangle $ABC$.