2017 IMO Shortlist G1

Let $A B C D E$ be a convex pentagon such that $A B=B C=C D, \angle E A B=\angle B C D$, and $\angle E D C=\angle C B A$. Prove that the perpendicular line from $E$ to $B C$ and the line segments $A C$ and $B D$ are concurrent. (Italy)

令 $A B C D E$ 为凸五边形，使得 $A B=B C=C D、\angle E A B=\angle B C D$ 和 $\angle E D C=\angle C B A$。证明$E$到$B C$的垂线与线段$A C$和$B D$是共线的。 (意大利)