2018 IMO Shortlist G1

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 $\overparen{A B}$ and $\overparen{A C}$ at points $F$ and $G$ respectively. Prove that $D E \| F G$. (Greece)

令$A B C$ 为外接圆$\Gamma$ 的锐角三角形。令$D$和$E$分别为线段$A B$和$A C$上的点，使得$A D=A E$。线段$B D$ 和$C E$ 的垂直平分线分别与小弧$\overparen{A B}$ 和$\overparen{A C}$ 相交于点$F$ 和$G$。证明 $D E \| F G$。 (希腊)