2007 IMO Shortlist G4

Consider five points $A, B, C, D, E$ such that $A B C D$ is a parallelogram and $B C E D$ is a cyclic quadrilateral. Let $\ell$ be a line passing through $A$, and let $\ell$ intersect segment $D C$ and line $B C$ at points $F$ and $G$, respectively. Suppose that $E F=E G=E C$. Prove that $\ell$ is the bisector of angle $D A B$. (Luxembourg)

考虑五个点 $A、B、C、D、E$，使得 $A B C D$ 是平行四边形，$B C E D$ 是循环四边形。设$\ell$为穿过$A$的直线，并令$\ell$与线段$D C$和线$B C$分别相交于点$F$和$G$。假设$EF=EG=E C$。证明$\ell$是角$D A B$的平分线。 (卢森堡)