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 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 $\angle A F C=\angle A B C=\angle D$,
$$
\angle A C F=\angle G C D \text {. }
$$

Therefore, $\triangle A C F \backsim \triangle G C D$
$$
\begin{array}{l}
\Rightarrow \angle G=\angle C A F=90^{\circ} \\
\Rightarrow C G \perp D E
\end{array}
$$
$\Rightarrow O_{1} G$ is the distance from point $O_{1}$ to $D E$
$$
\begin{array}{l}
\Rightarrow \frac{A C}{C F}=\frac{C G}{C D} \Rightarrow \frac{3}{2 \times 2}=\frac{2+O_{1} G}{3+6} \\
\Rightarrow O_{1} G=\frac{19}{4} .
\end{array}
$$