10. $A, B, C$ are three different points on circle $O$, and $\angle A O B=120^{\circ}$, point $C$ is within the minor arc $\overparen{A B}$ (point $C$ does not coincide with $A, B$), if $\overrightarrow{O C}=\lambda \overrightarrow{O A}+\mu \overrightarrow{O B}(\lambda, \mu \in \mathbf{R})$, then the range of $\lambda+\mu$ is $\qquad$ .
As shown in the figure, draw $O P \perp A B$, intersecting circle $O$ at point $P$. Let's assume the radius of circle $O$ is 1. Then
$$
\begin{array}{l}
\overrightarrow{O C}=\lambda \overrightarrow{O A}+\mu \overrightarrow{O B} \\
\Rightarrow \overrightarrow{O C} \cdot \overrightarrow{O P}=\lambda \overrightarrow{O A} \cdot \overrightarrow{O P}+\mu \overrightarrow{O B} \cdot \overrightarrow{O P} \\
\Rightarrow|O F|=(\lambda+\mu)|O Q| \Rightarrow \lambda+\mu=\frac{|O F|}{|O Q|} .
\end{array}
$$

Clearly, $|O Q|<|O F| \leqslant|O P|$ and $|O Q|=\frac{1}{2}$, so $\lambda+\mu \in(1,2]$.