ГДЗ по геометрии 8 класс Мерзляк Задание 482

\[Схематический\ рисунок.\]

\[Дано:\]

\[AC\ :BC = 1\ :4;\]

\[R = 8\ см;\ \]

\[AB = 9\ см.\]

\[Найти:\]

\[\text{OC.}\]

\[Решение.\]

\[OE = OF = R = 8;\]

\[CE = OC - OE = OC - 8;\]

\[CF = OF + OE + CE = OC + 8;\]

\[AB = BC - AC = 9;\]

\[BC - \frac{1}{4}BC = 9\ \ \]

\[\frac{3}{4}BC = 9\]

\[BC = \frac{4}{3} \bullet 9 = 12\ см.\ \ \ \]

\[AC = \frac{1}{4}BC = 3\ см.\]

\[CA \bullet CB = CE \bullet CF\]

\[3 \bullet 12 = (OC - 8)(OC + 8)\]

\[OC^{2} - 64 = 36\]

\[OC^{2} = 100\]

\[OC = \sqrt{100} = 10\ см.\]

\[Ответ:\ \ 10\ см.\]