Question 90
In triangle $ABC$, assume $a\gt b$, where $a=BC$ and $b=AC$. Let $M$ be the midpoint of $AB$, and let $\alpha,\beta$ be the incircles of triangles $ACM,BCM$, respectively. Let $A',B'$ be their points of tangency with $CM$. Prove that $A'B'=(a-b)/2$.