GR-HMS 2017 Problem 1

An acute triangle $ABC$ with $AB<AC<BC$ is inscribed in a circle $c(O,R)$ . The circle $c_1(A,AC)$ intersects the circle $c$ at point $D$ and intersects $CB$ at $E$ . If the line $AE$ intersects $c$ at $F$ and $G$ lies in $BC$ such that $EB=BG$ , prove that $F,E,D,G$ are concyclic.