KöMaL 2026 B5535

$a$, $b$ and $c$ are the sides and $r$ is the inradius of a scalene triangle. Let $s_a$ be the length of the median corresponding to side $a$, and let $t_a$ denote the distance of the incenter from the line of median $s_a$. Prove that $2t_as_a=|b-c|\cdot r.$