Решебник по геометрии 11 класс. Атанасян ФГОС 356

\[\boxed{\mathbf{356.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[Дано:\]

\[Доказательство.\]

\[⊿SO_{1}M_{1}\ подобен\ ⊿SOM;\ \ \]

\[O_{1}M_{1} = r;\ \ OM = R:\]

\[\frac{O_{1}M_{1}}{\text{OM}} = \frac{O_{1}S}{\text{OS}};\]

\[\frac{r}{R} = \frac{SO_{1}}{\text{SO}}.\]

\[S_{1} = \pi r^{2};\ \ S_{2} = \pi R^{2}:\]

\[\frac{r^{2}}{R^{2}} = \frac{SO_{1}^{2}}{SO^{2}};\]

\[\frac{S_{1}}{\pi}\ :\frac{S_{2}}{\pi} = \frac{SO_{1}^{2}}{SO^{2}}.\]

\[Что\ и\ требовалось\ доказать.\]