Question 97
A triangle $ABC$ has sides of lengths $AB = 50~\mathrm{cm}$, $BC = 20~\mathrm{cm}$ and $AC = 40~\mathrm{cm}$. Let $M$ and $N$ be points on the side $AB$ such that $CM$ is the bisector of the angle $\angle ACB$ and $CN$ is the altitude to the side $AB$. What is the length, in centimeters, of $MN$?