Question 100
Let $N$ be the foot of the altitude from $C$ to the hypotenuse $\overline{AB}$ of a right triangle $ABC$. The angle bisectors of the angles $\angle NCA$ and $\angle BCN$ intersect the segment $\overline{AB}$ in the points $K$ and $L$ respectively. If $S$ and $T$ are incircles of the triangles $BCN$ and $NCA$ respectively, prove that the quadrilateral $KLST$ is cyclic. (from an article of A. Marić)