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Консультация № 195705
24.05.2019, 08:11
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Здравствуйте! У меня возникли сложности с таким вопросом:
Точки M и N выбраны соответственно на основании BC и боковой стороне CD трапеции ABCD. Прямые AM и BN пересекаются в точке K, причём AK=4KM, KN=3BK. Найти отношение CN/ND.
Точки M и N выбраны соответственно на основании BC и боковой стороне CD трапеции ABCD. Прямые AM и BN пересекаются в точке K, причём AK=4KM, KN=3BK. Найти отношение CN/ND.
Обсуждение
25.05.2019, 14:14
общий
это ответ
Здравствуйте, Михаил!
Поясняющий решение рисунок находится в прикреплённом файле.
Проведём через точку N отрезок, параллельный отрезку BC до пересечения с отрезком AM в точке E. Тогда |EK|/|KN}=|KM|/|BK|, |KM|/|EK|=|BK|/|KN|=1/3, то есть |EK|=3|MK|. Кроме того, по условию, |AK|=4|MK|. Поэтому
Поясняющий решение рисунок находится в прикреплённом файле.
Проведём через точку N отрезок, параллельный отрезку BC до пересечения с отрезком AM в точке E. Тогда |EK|/|KN}=|KM|/|BK|, |KM|/|EK|=|BK|/|KN|=1/3, то есть |EK|=3|MK|. Кроме того, по условию, |AK|=4|MK|. Поэтому
|ME|=|MK|+|KE|=|MK|+|EK|=|MK|+3|MK|=4|MK|,
|AE|=|AK|-|EK|=4|MK|-3|MK|=|MK|,
|CN|/|ND|=|ME|/|EA|=|ME|/|AE|=4|MK|/|MK|=4/1.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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