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Консультация № 146360
07.10.2008, 18:05
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В окружности радиуса r проведена хорда длины r/2 . Через один конец хорды проведена касательная к этой окружности, а через другой - секущая, параллельная касательной. Найти расстояние между касательной и секущей.
Обсуждение
Неизвестный
08.10.2008, 04:22
общий
это ответ
Здравствуйте, Stepanov92!
У нас получается 3 треугольника, из которых 2 прямоугольных с общим катетом.
принимаем искомую величину за х (это как раз один из катетов малого треугольника)
Из теоремы пифагора выводим:
(R^2)/4-x^2=R^2-(R-x)^2
Упрощаем
(R^2)/4=2Rx
x=R/8
У нас получается 3 треугольника, из которых 2 прямоугольных с общим катетом.
принимаем искомую величину за х (это как раз один из катетов малого треугольника)
Из теоремы пифагора выводим:
(R^2)/4-x^2=R^2-(R-x)^2
Упрощаем
(R^2)/4=2Rx
x=R/8
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