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Консультация № 192373
12.01.2018, 14:57
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Мне нужно решить следующую задачу:
Продолжения противоположных сторон AB и CD вписанного четырёхугольника ABCD пересекаются в точке M, а сторон AD и BC – в точке N. Тогда а) биссектрисы углов AMD и ANB взаимно перпендикулярны; б) прямые MО и NО пересекают стороны четырехугольника в вершинах ромба; в) тогда точка пересечения О биссектрис этих углов лежит на отрезке, соединяющем середины диагоналей четырехугольника ABCD.
Причём пункты а) и б) я уже доказала, а вот пункт в) представляет большую трудность. Мне кажется, что я представляю, как нужно доказать, но никак не могу это сделать.
Мне нужно решить следующую задачу:
Продолжения противоположных сторон AB и CD вписанного четырёхугольника ABCD пересекаются в точке M, а сторон AD и BC – в точке N. Тогда а) биссектрисы углов AMD и ANB взаимно перпендикулярны; б) прямые MО и NО пересекают стороны четырехугольника в вершинах ромба; в) тогда точка пересечения О биссектрис этих углов лежит на отрезке, соединяющем середины диагоналей четырехугольника ABCD.
Причём пункты а) и б) я уже доказала, а вот пункт в) представляет большую трудность. Мне кажется, что я представляю, как нужно доказать, но никак не могу это сделать.
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