Question 30
Let $ABC$ be an isosceles triangle with $AC = BC$. Points $D$, $E$, $F$ are considered in $BC$, $CA$, $AB$, respectively, such that $AF \gt BF$ and the quadrilateral $CEFD$ is a parallelogram. The line perpendicular to $BC$ drawn by $B$ intersects the bisector of $AB$ at $G$. Prove that the line $DE$ is perpendicular to the line $FG$.