Question 94
Let $ABC$ be a triangle, and let $J$ be the center of its $A$-excircle. This circle touches segment $BC$ at $M$, and the lines $AB$ and $AC$ and $AC$ at $K,L$. Let $F=LM\cap BJ$ and $G=KM\cap CJ$. Let $S=AF\cap BC$ and $T=AG\cap BC$. Prove that $M$ is the midpoint of $ST$.