Question 92
Let $\Omega$ be the circumcircle of an acute-angled triangle $ABC$. Points $D, E, F$ are the midpoints of the inferior arcs $BC, CA, AB$, respectively, on $\Omega$. Let $G$ be the point diametrically opposed to $D$ on $\Omega$. Let $X$ be the intersection of lines $GE$ and $AB$, while $Y$ the intersection of lines $FG$ and $CA$. Let the circumcenters of triangles $BEX$ and $CFY$ be points $S$ and $T$, respectively. Prove that $D, S, T$ are collinear.