Решебник по геометрии 8 класс Мерзляк Задание 323

\[Рисунок\ в\ учебнике.\]

\[Дано:\]

\[P_{\text{PAI}} = P_{1};\]

\[P_{\text{JBL}} = P_{2};\]

\[P_{\text{TCN}} = P_{3}.\]

\[Найти:\]

\[P_{\text{ABC}}.\]

\[Решение.\]

\[1)\ Окружность:\]

\[IG = IG;\]

\[JE = JD;\]

\[LD = LF;\]

\[TF = TH;\]

\[NH = Nk;\]

\[PK = PG.\]

\[2)\ В\ \mathrm{\Delta}PAI:\]

\[P_{\text{PAI}} = AP + AI = PI = P_{1}.\]

\[3)\ В\ \mathrm{\Delta}JBL:\]

\[P_{\text{JBL}} = BJ + BL + JL = P_{2}.\]

\[4)\ В\ \mathrm{\Delta}TCN:\]

\[P_{\text{TCN}} = CT + CN + TN = P_{3}.\]

\[5)\ В\ \mathrm{\Delta}ABC:\]

\(Ответ:\ \ P_{1} + P_{2} + P_{3}.\)