2020 APMO 第 1 题

Let $\Gamma$ be the circumcircle of $\triangle A B C$. Let $D$ be a point on the side $B C$. The tangent to $\Gamma$ at $A$ intersects the parallel line to $B A$ through $D$ at point $E$. The segment $C E$ intersects $\Gamma$ again at $F$. Suppose $B, D, F, E$ are concyclic. Prove that $A C, B F, D E$ are concurrent.

令$\Gamma$ 为$\triangle A B C$ 的外接圆。 Let $D$ be a point on the side $B C$. $\Gamma$ 在 $A$ 处的切线与通过 $D$ 到 $B A$ 的平行线在点 $E$ 处相交。线段$C E$ 再次与$\Gamma$ 相交于$F$。 Suppose $B, D, F, E$ are concyclic. Prove that $A C, B F, D E$ are concurrent.