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Консультация № 137088
16.05.2008, 15:53
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В параллелограмме ABCD диагонали пересекаются в точке O.Периметр треугольника OBC на 6 см больше периметра треугольника OCD.Сторона BC пересекает биссектрису BAD в точке M так,что BM:MC=5:3.Найдите стороны и периметр ABCD
Обсуждение
Неизвестный
16.05.2008, 17:54
общий
это ответ
Здравствуйте, Волков Алексеей Валерьевич!
Треугольник АВМ - равнобедренный, так как углы при основании равны (угол ВАМ = углу МАД = углу ВМА), тогда если принять за х одну часть, то ВМ = 5х, МС = 3х, АВ = СД = 5х. Найдем разность периметров:
(ВС + СО + ВО) - (СО + СД + ДО) = 6
8х - 5х = 6
3х = 6
х = 2
ВС = 8х = 16
СД = 5х = 10
периметр = 2*(10 + 16) = 52
Треугольник АВМ - равнобедренный, так как углы при основании равны (угол ВАМ = углу МАД = углу ВМА), тогда если принять за х одну часть, то ВМ = 5х, МС = 3х, АВ = СД = 5х. Найдем разность периметров:
(ВС + СО + ВО) - (СО + СД + ДО) = 6
8х - 5х = 6
3х = 6
х = 2
ВС = 8х = 16
СД = 5х = 10
периметр = 2*(10 + 16) = 52
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