Distance Between Two Perpendicular Feet in a Triangle
Geometry · problem by Russelle G.
In triangle $ABC$, $AB = 125$, $AC = 117$, and $BC = 120$. The angle bisector of $\angle A$ intersects $BC$ at point $L$, and the angle bisector of $\angle B$ intersects $AC$ at point $K$. Let $M$ and $N$ be the feet of the perpendiculars from $C$ to $BK$ and $AL$, respectively. Find $MN$.