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Консультация № 180700
12.11.2010, 20:45
65.91 руб.
0
5
1
Здравствуйте,уважаемые эксперты.Помогите,пожалуйста решить задачу.Длины сторон треугольника ABC-последовательные целые числа,а медиана,проведенная из вершины A,перпендикулярна биссектрисе угла B.Найдите длины сторон треугольника ABC.Заранее благодарен.
Обсуждение
12.11.2010, 21:37
общий
13.11.2010, 12:32
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
АМ - медиана.
О - точка пересечения медианы и биссектрисы.
треугольники АОВ и ВОМ равны согласно второму признаку равенства треугольников (сторона ОВ общая и равны прилегающие к ней углы), а поэтому АВ=ВМ=ВС/2.
Это возможно лишь в случаях (учитывая, что стороны есть целые последовательные числа):
1) АВ=1 и ВС=2. Соответственно АС=3. Но такого треугольника не бывает (в силу теоремы о неравенстве треугольника: "Во всяком треугольнике всякая сторона меньше суммы двух других сторон").
2) АВ=2 и ВС=4. Соответственно АС=3.
Ответ: |AB| = 2, |AC| = 3, |BC| = 4.
АМ - медиана.
О - точка пересечения медианы и биссектрисы.
треугольники АОВ и ВОМ равны согласно второму признаку равенства треугольников (сторона ОВ общая и равны прилегающие к ней углы), а поэтому АВ=ВМ=ВС/2.
Это возможно лишь в случаях (учитывая, что стороны есть целые последовательные числа):
1) АВ=1 и ВС=2. Соответственно АС=3. Но такого треугольника не бывает (в силу теоремы о неравенстве треугольника: "Во всяком треугольнике всякая сторона меньше суммы двух других сторон").
2) АВ=2 и ВС=4. Соответственно АС=3.
Ответ: |AB| = 2, |AC| = 3, |BC| = 4.
4
Неизвестный
12.11.2010, 21:40
общий
Адресаты:
Если АВ=1, ВС=2, АС=3, тогда получается, что это прямая.
13.11.2010, 00:11
общий
Адресаты:
Здравствуйте, Роман!
Было бы неплохо, если бы Вы более детально объяснили своё решение. Желательно, используя такие неоспоримые факты, как теоремы синусов и косинусов, Пифагора и т. д. А то как-то непонятно...
С уважением.
Было бы неплохо, если бы Вы более детально объяснили своё решение. Желательно, используя такие неоспоримые факты, как теоремы синусов и косинусов, Пифагора и т. д. А то как-то непонятно...
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
13.11.2010, 11:15
общий
Гордиенко Андрей Владимирович Роман Селиверстов:
Здравствуйте, Роман!
Было бы неплохо, если бы Вы более детально объяснили своё решение. Желательно, используя такие неоспоримые факты, как теоремы синусов и косинусов, Пифагора и т. д. А то как-то непонятно...
С уважением.
Ответ дополнил.
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