Question 2
In an isosceles triangle $ABC$, $AB = AC$. Let $E$ be a point on $AC$ and extend $AB$ to a point $D$ such that $BD = EC$. Let $F$ be the intersection of $BC$ and $DE$ and let the circumcircle of $ABC$ intersect the circumcircle of $BDF$ at $G$. Prove that $DE$ is perpendicular to $FG$.