Question 88
Let $ABC$ be an acute triangle with circumcircle $\Omega$. Let $B_{0}$ be the midpoint of $AC$ and let $C_{0}$ be the midpoint of $AB$. Let $D$ be the foot of the altitude from $A$, and let $G$ be the centroid of the triangle $ABC$. Let $\omega$ be a circle through $B_{0}$ and $C_{0}$ that is tangent to the circle $\Omega$ at a point $X \neq A$. Prove that the points $D$, $G$, and $X$ are collinear.