Question 101
Let $\triangle ABC$ be a triangle with centroid $G$. Let $D$, $E$ and $F$ be the circumcenters of $\triangle BCG$, $\triangle CAG$ and $\triangle ABG$, respectively. The point $X$ is defined as the intersection of the perpendiculars from $E$ to $AB$ and $F$ to $AC$. Prove that $DX$ bisects the segment $EF$.