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Консультация № 196176
21.08.2019, 21:32
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Здравствуйте! Прошу помощи в следующем вопросе:
Две окружности вписаны в один угол, первая касается одной
стороны угла в точке A, вторая касается другой стороны угла в точке B.
а) Докажите, что на отрезке AB окружности высекают равные хорды.
б) Найдите косинус угла, если одна из окружностей в 2 раза больше
другой, а треть отрезка AB находится вне данных окружностей.
а) решила по теореме о касательной и секущей , а б) что-то ни как.
Две окружности вписаны в один угол, первая касается одной
стороны угла в точке A, вторая касается другой стороны угла в точке B.
а) Докажите, что на отрезке AB окружности высекают равные хорды.
б) Найдите косинус угла, если одна из окружностей в 2 раза больше
другой, а треть отрезка AB находится вне данных окружностей.
а) решила по теореме о касательной и секущей , а б) что-то ни как.
Обсуждение
22.08.2019, 18:45
общий
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Здравствуйте, Mari! Я предлагаю Вам для начала обсуждения второго пункта задания выполнить аккуратный рисунок и показать его здесь. 
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.08.2019, 21:33
общий
Адресаты:
Как Вы полагаете, точки 
расположены на одной прямой?
расположены на одной прямой?
Об авторе:
Facta loquuntur.
Facta loquuntur.
23.08.2019, 07:01
общий
25.08.2019, 06:04
Адресаты:
Здравствуйте, Mari!
Пусть СА = b, CB = 2b (так как CB = CB1 как отрезки касательных к одной окружности)
Пусть AM=MM1=M1B = h
По теореме косинусов для треугольника АВС получаем
(*)
т.к АВ - секущая, а АВ1 - касательная, то
тогда
Пусть СА = b, CB = 2b (так как CB = CB1 как отрезки касательных к одной окружности)
Пусть AM=MM1=M1B = h
По теореме косинусов для треугольника АВС получаем
(*)т.к АВ - секущая, а АВ1 - касательная, то
тогда
23.08.2019, 07:10
общий
Адресаты:
Для решения задачи используются свойства отрезков касательных, соотношение отрезков секущей и касательной и теорема косинусов. В целом задача несложная, но нужно внимательно читать условия. Я сначала неверно истолковала условия. Теперь все верно 
23.08.2019, 07:16
общий
23.08.2019, 07:19
Адресаты:
Mari Да на одной
И в силу соображений симметрии точка
расположена на биссектрисе угла, косинус которого требуется вычислить...Как по-Вашему, через какие величины нужно выразить искомый косинус?
P. S. Пока я пытался подвести Вас к самостоятельному решению задачи, меня опередили, предложив Вам готовое решение. Я не стану его проверять...
Об авторе:
Facta loquuntur.
Facta loquuntur.
23.08.2019, 17:16
общий
23.08.2019, 17:18
Спасибо большое.Все понятно. Только в решении есть описки.
24.08.2019, 05:16
общий
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Исправила. В одном месте вместо М1 было набрано Н1. А где еще? Описки - это множественное число 
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