10.285. In a circle of radius $R$, two parallel chords are drawn on opposite sides of the center, one of which subtends an arc of $60^{\circ}$, the other $120^{\circ}$. Find the area of the part of the circle enclosed between the chords.
## Solution.

The area of the segment with an arc of $60^{\circ}$ is $S_{1}=\frac{\pi R^{2}}{6}-\frac{R^{2} \sqrt{3}}{4}$, and the area of the segment with an arc of $120^{\circ}$ is $S_{2}=\frac{\pi R^{2}}{3}-\frac{R^{2} \sqrt{3}}{4}$. The desired area is

$$
\begin{gathered}
S=\pi R^{2}-S_{1}-S_{2}=\frac{R^{2}(\pi+\sqrt{3})}{2} . \\
\text { Answer: } \frac{R^{2}(\pi+\sqrt{3})}{2}
\end{gathered}
$$