Question 4
In triangle $ABC,$ $AB = 125,$ $AC = 117,$ and $BC = 120.$ The angle bisector of angle $A$ intersects $\overline{BC}$ at point $L,$ and the angle bisector of angle $B$ intersects $\overline{AC}$ at point $K.$ Let $M$ and $N$ be the feet of the perpendiculars from $C$ to $\overline{BK}$ and $\overline{AL},$ respectively. Find $MN.$