6. As shown in Figure 1, given that $\odot O_{1}$ and $\odot O_{2}$ intersect at points $A$ and $B$, point $C$ is on $\odot O_{1}$ and outside $\odot O_{2}$, the extensions of $C A$ and $C B$ intersect $\odot O_{2}$ at points $D$ and $E$, respectively, with $A C=3$, $A D=6$, and the radius of $\odot O_{1}$ is 2. Then

Figure 1 The distance from point $O_{1}$ to $D E$ is ().
(A) $\frac{17}{4}$
(B) $\frac{9}{2}$
(C) $\frac{19}{4}$
(D) 5
6. C.

Connect $C O_{1}$ and extend it to intersect $\odot O_{1}$ at point $F$, and intersect $D E$ at point $G$. Connect $A B$ and $A F$.
Then $\angle A F C = \angle A B C = \angle D$,
$\angle A C F = \angle G C D$.
Therefore, $\triangle A C F \backsim \triangle G C D$
$\Rightarrow \angle G = \angle C A F = 90^{\circ}$
$\Rightarrow C G \perp D E$
$\Rightarrow O_{1} G$ is the distance from point $O_{1}$ to $D E$
$\Rightarrow \frac{A C}{C F} = \frac{C G}{C D} \Rightarrow \frac{3}{2 \times 2} = \frac{2 + O_{1} G}{3 + 6}$
$\Rightarrow O_{1} G = \frac{19}{4}$.