Question 15
Let $A B C$ be an acute-angled triangle with circumcircle $\Gamma$. Let $D$ and $E$ be points on the segments $A B$ and $A C$, respectively, such that $A D=A E$. The perpendicular bisectors of the segments $B D$ and $C E$ intersect the small arcs $\overset{\frown}{A B}$ and $\overset{\frown}{A C}$ at points $F$ and $G$ respectively. Prove that $D E \| F G$.