jmc

Extend $CM$ and $CN$ such that they intersect line $AB$ at points $P$ and $Q$, respectively. Since $BM$ is the angle bisector of angle $B$, and $CM$ is perpendicular to $BM$, so $BP=BC=120$, and $M$ is the midpoint of $CP$. For the same reason, $AQ=AC=117$, and $N$ is the midpoint of $CQ$. Hence $MN=\frac{PQ}{2}$. $PQ=BP+AQ-AB=120+117-125=112$, so $MN=\boxed{56}$.