2019 IMO Shortlist G1

Let $A B C$ be a triangle. Circle $\Gamma$ passes through $A$, meets segments $A B$ and $A C$ again at points $D$ and $E$ respectively, and intersects segment $B C$ at $F$ and $G$ such that $F$ lies between $B$ and $G$. The tangent to circle $B D F$ at $F$ and the tangent to circle $C E G$ at $G$ meet at point $T$. Suppose that points $A$ and $T$ are distinct. Prove that line $A T$ is parallel to $B C$. (Nigeria)

设 $A B C$ 为三角形。圆$\Gamma$穿过$A$，分别在$D$和$E$处再次与线段$A B$和$A C$相交，并在$F$和$G$处与线段$B C$相交，使得$F$位于$B$和$G$之间。圆 $B D F$ 在 $F$ 处的切线和圆 $C E G$ 在 $G$ 处的切线在点 $T$ 处相交。假设点 $A$ 和 $T$ 不同。证明线$A T$ 与$B C$ 平行。 (尼日利亚)