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Консультация № 196686
16.10.2019, 17:13
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Здравствуйте! У меня возникли сложности с таким вопросом:
Окружности с центрами P и Q пересекаются в точках A и B; при этом угол APB=60,угол AQB=30. Найдите радиусы окружности, если PQ=a
Окружности с центрами P и Q пересекаются в точках A и B; при этом угол APB=60,угол AQB=30. Найдите радиусы окружности, если PQ=a
Обсуждение
20.10.2019, 19:40
общий
это ответ
Здравствуйте, sasha.yakimova9976@gmail.com!
Возможны два случая: в первом случае точки
и 
расположены по разные стороны от прямой 
во втором случае -- по одну сторону. Эти случаи изображены соответственно на верхнем и нижнем рисунках в прикреплённом файле.
Случай 1
Обозначим через
точку пересечения отрезков 
и 
В силу симметрии относительно прямой 
точка 
делит отрезок пополам. Угол 
имеет величину 
Отрезки и взаимно перпендикулярны.
Обозначим
В треугольнике по теореме косинусов
В прямоугольном треугольнике
В прямоугольном треугольнике
[1, с. 107]. 
Исходя из формул (2) и (3), получим
Подставляя выражение для
в формулу (1), получим
Случай 2
Действуя аналогично рассмотренному выше, получим
Литература
1. Цыпкин А. Г., Цыпкин Г. Г. Математические формулы. -- М.: Наука, 1985. -- 128 с.
Возможны два случая: в первом случае точки
и расположены по разные стороны от прямой во втором случае -- по одну сторону. Эти случаи изображены соответственно на верхнем и нижнем рисунках в прикреплённом файле.Случай 1
Обозначим через
точку пересечения отрезков и В силу симметрии относительно прямой точка делит отрезок пополам. Угол имеет величину Отрезки и взаимно перпендикулярны.Обозначим
В треугольнике по теореме косинусовВ прямоугольном треугольнике
В прямоугольном треугольнике
[1, с. 107]. Исходя из формул (2) и (3), получим
Подставляя выражение для
в формулу (1), получимСлучай 2
Действуя аналогично рассмотренному выше, получим
Литература
1. Цыпкин А. Г., Цыпкин Г. Г. Математические формулы. -- М.: Наука, 1985. -- 128 с.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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