1. In $\triangle A B C$, $O$ is the circumcenter of $\triangle A B C$, and it satisfies $\overrightarrow{A O} \cdot \overrightarrow{A B}+\overrightarrow{B O} \cdot \overrightarrow{B C}=\overrightarrow{C O} \cdot \overrightarrow{C A}$. Then the size of $\angle B$ is . $\qquad$
$-1 . \frac{\pi}{2}$.
Given that $O$ is the circumcenter of $\triangle A B C$, we have
$$
\begin{array}{l}
\overrightarrow{A O} \cdot \overrightarrow{A B}=\frac{1}{2} c^{2} \\
\overrightarrow{B O} \cdot \overrightarrow{B C}=\frac{1}{2} a^{2} \\
\overrightarrow{C O} \cdot \overrightarrow{C A}=\frac{1}{2} b^{2}
\end{array}
$$

Thus $a^{2}+c^{2}=b^{2} \Rightarrow \angle B=\frac{\pi}{2}$.