Предмет: Геометрия, автор: КиСа009

Точки M и N делят сторону BC треугольника ABC на три равные части, причём M лежит ближе к B. Прямая, параллельная стороне AC, пересекает отрезки AB, AM и AN в точках D, E и F соответственно. Найдите отношение DE:EF.

Ответы

Автор ответа: siestarjoki
0

GN||DF => GH/HN =DE/EF (соответствующие отрезки в подобных треугольниках GAN и DAF)

Теорема Фалеса

BG/GA =BN/NC =2/1

GA/AB =1/3

Теорема Менелая

BM/MN *NH/HG *GA/AB =1

1/1 *NH/HG *1/3 =1 => GH/HN =1/3 =DE/EF

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