Question 13
G1 (FRA) A semicircle $\Gamma$ is drawn on one side of a straight line $l$. $C$ and $D$ are points on $\Gamma$. The tangents to $\Gamma$ at $C$ and $D$ meet $l$ at $B$ and $A$ respectively, with the center of the semicircle between them. Let $E$ be the point of intersection of $AC$ and $BD$, and $F$ the point on $l$ such that $EF$ is perpendicular to $l$. Prove that $EF$ bisects $\angle CFD$.