2017 IMO Shortlist G5

Let $A B C C_{1} B_{1} A_{1}$ be a convex hexagon such that $A B=B C$, and suppose that the line segments $A A_{1}, B B_{1}$, and $C C_{1}$ have the same perpendicular bisector. Let the diagonals $A C_{1}$ and $A_{1} C$ meet at $D$, and denote by $\omega$ the circle $A B C$. Let $\omega$ intersect the circle $A_{1} B C_{1}$ again at $E \neq B$. Prove that the lines $B B_{1}$ and $D E$ intersect on $\omega$. (Ukraine)

令$A B C C_{1} B_{1} A_{1}$ 为凸六边形，使得$A B=B C$，并假设线段$A A_{1}、B B_{1}$ 和$C C_{1}$ 具有相同的垂直平分线。设对角线$A C_{1}$ 和$A_{1} C$ 交于$D$，并用$\omega$ 表示圆$A B C$。让$\omega$ 再次与圆$A_{1} B C_{1}$ 相交于$E \neq B$。证明线 $B B_{1}$ 和 $D E$ 相交于 $\omega$。 (乌克兰)