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Консультация № 196120
14.08.2019, 16:05
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Окружность с диаметром AB пересекается с окружностью с
центром B в точках M и N.
а) Докажите, что если окружности равны, то диаметр первой из них,
проходящий через точку N, делит хорду AM пополам.
б) Пусть радиус первой окружности вдвое больше радиуса второй. В
каком отношении диаметр первой окружности, проходящий через точ-
ку N, делит хорду AM Вроде с а) понятно, а бы что-то кручу чертёж и ни как.....
Окружность с диаметром AB пересекается с окружностью с
центром B в точках M и N.
а) Докажите, что если окружности равны, то диаметр первой из них,
проходящий через точку N, делит хорду AM пополам.
б) Пусть радиус первой окружности вдвое больше радиуса второй. В
каком отношении диаметр первой окружности, проходящий через точ-
ку N, делит хорду AM Вроде с а) понятно, а бы что-то кручу чертёж и ни как.....
Обсуждение
14.08.2019, 20:56
общий
16.08.2019, 12:59
это ответ
Здравствуйте, Mari!
a)
равносторонние, значит 
вертикальные, значит 
OF - биссектриса равностороннего треугольника, значит ОF - медиана, значит AF = FM
б) AB = 4r, BM = r,
прямоугольный 
Из
Из
значит 
по т. Менелая : рассматривая треугольник AMQ и прямую (NOF), идущую через продолжение стороны MQ, получаем
a)
равносторонние, значит вертикальные, значит OF - биссектриса равностороннего треугольника, значит ОF - медиана, значит AF = FM
б) AB = 4r, BM = r,
прямоугольный Из
Из
значит по т. Менелая : рассматривая треугольник AMQ и прямую (NOF), идущую через продолжение стороны MQ, получаем
5
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