Question 110
A triangle $A B C$ is given. On side $A C$ lie points $D$ and $E$ such that the order of the points on this line is $A, E, D, C$. The line through $E$ parallel to $B C$ intersects the circumcircle of $\triangle A B D$ at a point $F$, where $E$ and $F$ lie on opposite sides of $A B$. The line through $E$ parallel to $A B$ intersects the circumcircle of $\triangle B C D$ at a point $G$, where $E$ and $G$ lie on opposite sides of $B C$. Prove that $D E F G$ is a cyclic quadrilateral.
