(8) As shown in the figure, in $\triangle A B C$, $A B=3, A C=$ 5. If $O$ is the circumcenter of $\triangle A B C$, then the value of $\overrightarrow{A O} \cdot \overrightarrow{B C}$ is $\qquad$
88 Prompt: As shown in the figure, let $D$ be the midpoint of $B C$, and connect $O D, A D$, then $O D \perp B C$. Therefore,
$$
\begin{aligned}
\overrightarrow{A O} \cdot \overrightarrow{B C} & =(\overrightarrow{A D}+\overrightarrow{D O}) \cdot \overrightarrow{B C} \\
& =\overrightarrow{A D} \cdot \overrightarrow{B C}+\overrightarrow{D O} \cdot \overrightarrow{B C} \\
& =\overrightarrow{A D} \cdot \overrightarrow{B C} \\
& =\frac{1}{2}(\overrightarrow{A C}+\overrightarrow{A B}) \cdot(\overrightarrow{A C}-\overrightarrow{A B}) \\
& =\frac{1}{2}\left(|\overrightarrow{A C}|^{2}-|\overrightarrow{A B}|^{2}\right)=8 .
\end{aligned}
$$