ГДЗ по геометрии 9 класс Мерзляк Задание 242

\[R = \frac{a}{2\sin\frac{180{^\circ}}{3}} = \frac{a}{2\sin{60{^\circ}}} =\]

\[= \frac{a}{2}\ :\frac{\sqrt{3}}{2} = \frac{a}{\sqrt{3}}.\]

\[C = 2\pi R = 2\pi \bullet \frac{a}{\sqrt{3}} = \frac{2\pi a}{\sqrt{3}} =\]

\[= \frac{2\pi\sqrt{3}}{3}\text{a.}\]

\[Ответ:\ \ \frac{2\pi\sqrt{3}}{3}\text{a.}\]