Three equal circles are described with vertices of the triangles as centres. If the radius of each circle is… · ABC26GN4658

We have: $$\begin{aligned} \text { Required area } & =\frac{\pi r^{2} \theta_{1}}{360}+\frac{\pi r^{2} \theta_{2}}{360}+\frac{\pi r^{2} \theta_{3}}{360} \\ & =\frac{\pi r^{2}}{360}\left(\theta_{1}+\theta_{2}+\theta_{3}\right) \\ & =\frac{\pi r^{2} \times 180}{360}=\frac{\pi r^{2}}{2} \cdot\left[\because \theta_{1}+\theta_{2}+\theta_{3}=180^{\circ}\right] \end{aligned}$$