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Консультация № 194045
30.11.2018, 19:06
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Здравствуйте, уважаемые эксперты!
Попалась мне на глаза такая задача
Окружность радиуса 2sqrt(3) касается сторон BC и AC треугольника ABC в точках P и K соответственно и пересекает сторону AB в точках M и N (N лежит между B и M) так, что отрезок MP параллелен AC, CK=2, BK=6. Найдите угол ВСА, АС и площадь треугольника BKN.
Решение:
Угол BCA равен 120 градусов, это просто доказывается.
Так же на чертеже я показала все, что нашла.
А дальше, судя по построению в реальном размере исходя из данных задачи центр окружности должен лежать на стороне MN, но я что-то затрудняюсь , как это доказать.
Была бы признательна за подсказку
Попалась мне на глаза такая задача
Окружность радиуса 2sqrt(3) касается сторон BC и AC треугольника ABC в точках P и K соответственно и пересекает сторону AB в точках M и N (N лежит между B и M) так, что отрезок MP параллелен AC, CK=2, BK=6. Найдите угол ВСА, АС и площадь треугольника BKN.
Решение:
Угол BCA равен 120 градусов, это просто доказывается.
Так же на чертеже я показала все, что нашла.
А дальше, судя по построению в реальном размере исходя из данных задачи центр окружности должен лежать на стороне MN, но я что-то затрудняюсь , как это доказать.
Была бы признательна за подсказку
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Обсуждение
04.12.2018, 20:26
общий
Центр окружности находится на АВ. Треугольник получается равнобедренный. Для него все считается. И угол ВСА, и АС, и площадь треугольника BKN.
Если рассмотреть ситуацию, что центр не лежит на АВ. Тогда Нарушается условие параллельности МР стороне АС.. Через точку Р можно провести только одну параллельную прямую данной прямой.
Если рассмотреть ситуацию, что центр не лежит на АВ. Тогда Нарушается условие параллельности МР стороне АС.. Через точку Р можно провести только одну параллельную прямую данной прямой.
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