две окружности радиусов R=3 и r=1 касаются внешним образом найдите расстояния от точки касания окружностей до их общих касательных
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ГеометрияАвтор:
hayleevkzkИз рисунка видно, что мы имеем прямоугольную трапецию с основаниями АО₁ = 3
и ВО₂ = 1 и линией параллельной им СD. Проведем линию ЕО₂ параллельную касательной и получим подобные треугольники О₁ЕО₂ и FDO₂. Исходя из подобия треугольников составим пропорцию.
DF/EO₁ = O₂D/O₁O₂
DF = EO₁*O₂D/O₁O₂ = (3-1)*1/(3+1) = 2/4 = 0,5
CF = BO₂ = 1
CD = CF + DF = 1 + 0,5 = 1,5
Ответ: расстояние СD от точки касания окружностей до касательной 1,5
Автор:
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