Question 168
In $\triangle XYZ$, let $A$ be a point on (segment) $YZ$ such that $XA$ is perpendicular to $YZ$. Let $M$ and $N$ be the incenters of triangles $XYA$ and $XZA$, respectively. If $YZ = 28$, $XA = 24$, and $YA = 10$, what is the length of $MN$?