Question 113
Let $ABC$ be a triangle and let $M$ be the midpoint of the side $BC$. The parallels through $M$ to $AB$ and $AC$ cross the tangent at $A$ to circle $ABC$ at $X$ and $Y$, respectively. The circles $BMX$ and $CMY$ cross again at $S$. Prove that the circles $SXY$ and $SBC$ are tangent.
