MathNet 2022-part-03 — 197 problems (EN–VI) Question 103

In triangle $A B C$, the point $M$ is the midpoint of side $B C$. On the bisector of angle $B A C$, the point $N$ is taken such that $B N \perp A N$. Determine the length of side $A C$ if $A B=10~\mathrm{cm}$ and $M N=2~\mathrm{cm}$.