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Консультация № 144773
23.09.2008, 16:52
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Площадь кольца между двумя концентрическими окружностями равна 9π см². Найти длину хорды большей окружности, касающейся меньшей окружности. 
Обсуждение
Неизвестный
24.09.2008, 05:19
общий
26.09.2008, 09:31
это ответ
Здравствуйте, Олег Валерьевич!
R и r - радисы окружностей
Х - искомая длина хорды
при построении радиусов к тоскам пересечения и касания хорды с окружностями получается прямоугольный треугольник, где:
R^2=r^2+(x/2)^2
отсюда x=2*sqrt(R^2-r^2) (1)
Вернемся к известным данным.
Площадь кольца - R^2*п-r^2*п=9п
Из этого влегкую выводим R^2=9+r^2 (2)
Подставляем выражение (2) в (1) и получаем:
Х=2*sqrt(9)=6.
Осталось подставить пи и посчитать.
sqrt - корень квадратный.
R и r - радисы окружностей
Х - искомая длина хорды
при построении радиусов к тоскам пересечения и касания хорды с окружностями получается прямоугольный треугольник, где:
R^2=r^2+(x/2)^2
отсюда x=2*sqrt(R^2-r^2) (1)
Вернемся к известным данным.
Площадь кольца - R^2*п-r^2*п=9п
Из этого влегкую выводим R^2=9+r^2 (2)
Подставляем выражение (2) в (1) и получаем:
Х=2*sqrt(9)=6.
Осталось подставить пи и посчитать.
sqrt - корень квадратный.
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