Question 62
Let $ABCDE$ be a convex pentagon inscribed in a circle $\omega$ such that $CD \parallel BE$. The line tangent to $\omega$ at $B$ intersects the line $AC$ at a point $F$ such that $A$ lies between the points $C$ and $F$. The lines $BD$ and $AE$ intersect at $G$. Prove that the line $FG$ is tangent to the circumcircle of $ADG$.