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Консультация № 190747
19.03.2017, 04:59
0.00 руб.
24.03.2017, 15:32
1
6
1
Здравствуйте! Прошу помощи в следующем вопросе:
В [$916$]ABC (AB=BC) медианы пересекаются в точке O и BO=24 см, AO=9[$8730$]2 см. Через точку O параллельно отрезку AC проходит прямая l. Вычислить длину отрезка прямой l, заключённого между отрезками AB и BC в [$916$]ABC.
В [$916$]ABC (AB=BC) медианы пересекаются в точке O и BO=24 см, AO=9[$8730$]2 см. Через точку O параллельно отрезку AC проходит прямая l. Вычислить длину отрезка прямой l, заключённого между отрезками AB и BC в [$916$]ABC.
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Обсуждение
19.03.2017, 08:57
общий
это ответ
Здравствуйте, svrvsvrv!
Обозначим
- искомая длина В равнобедренном треугольнике медиана, проведённая к основанию, является высотой, и по теореме Пифагора, учитывая свойство точки пересечения медиан,
В силу подобия соответствующих треугольников,
откуда
(см).
Обозначим
- искомая длина В равнобедренном треугольнике медиана, проведённая к основанию, является высотой, и по теореме Пифагора, учитывая свойство точки пересечения медиан,В силу подобия соответствующих треугольников,
откуда (см).
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
19.03.2017, 09:47
общий
Адресаты:
svrvsvrv Речь идёт о подобии треугольников АВС и DBN? Как получилось 3BO/2?
В условии задачи и в моём решении нет треугольника DBN. Речь идёт о подобии двух равнобедренных треугольников - с основаниями, имеющими длины
и 
соответственно. Множитель 
- это отношение длины медианы к длине её отрезка 
(согласно свойству точки пересечения медиан).Эту задачу я решал в уме, без рисунка...
Об авторе:
Facta loquuntur.
Facta loquuntur.
24.03.2017, 15:27
общий
Адресаты:
Гордиенко Андрей Владимирович Эту задачу я решал в уме, без рисунка...
24.03.2017, 15:33
общий
Адресаты:
Интересующий Вас отрезок проходит через точку пересечения медиан параллельно основанию - отрезку 
- равнобедренного треугольника. Об этом говорится в условии задачи.
- равнобедренного треугольника. Об этом говорится в условии задачи.
Об авторе:
Facta loquuntur.
Facta loquuntur.
24.03.2017, 15:52
общий
24.03.2017, 15:54
Адресаты:
Гордиенко Андрей Владимирович Об этом говорится в условии задачи.
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