Question 28
Let $D$ be a point on the side $BC$ of an acute triangle $ABC$ and let $E$ be a point on the line segment $AD$. Let $F$ and $G$ be the feet of the altitudes drawn from the vertex $D$ in triangles $ABD$ and $ACD$, respectively. The line $BE$ intersects the circumcircle of the triangle $DEG$ at point $H \neq E$. Prove that points $B, F, G$ and $H$ are concyclic.