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Консультация № 195398
28.04.2019, 00:06
0.00 руб.
0
4
1
Здравствуйте! У меня возникли сложности с таким вопросом:
На плоскости отметили несколько точек, никакие три из которых не лежат на
одной прямой.
1) Сколько точек могли отметить, если известно, что любой треугольник с
вершинами в отмеченных точках будет непременно прямоугольным. Найдите
все ответы и докажите, что других нет.
На плоскости отметили несколько точек, никакие три из которых не лежат на
одной прямой.
1) Сколько точек могли отметить, если известно, что любой треугольник с
вершинами в отмеченных точках будет непременно прямоугольным. Найдите
все ответы и докажите, что других нет.
Обсуждение
28.04.2019, 00:27
общий
Адресаты:
Я предполагаю, что могли отметить или три, или четыре точки, причём во втором случае эти точки расположены в вершинах квадрата. А каково Ваше мнение?
Об авторе:
Facta loquuntur.
Facta loquuntur.
28.04.2019, 01:05
общий
28.04.2019, 01:08
Адресаты:
Да насчёт квадрата, действительно может, но надо же доказать что больше точек быть не может.
28.04.2019, 06:26
общий
Адресаты:
Да, надо доказать. Попробуйте: по-моему, это нетрудно. 
Об авторе:
Facta loquuntur.
Facta loquuntur.
29.04.2019, 11:08
общий
это ответ
Здравствуйте, alexs00035@gmail.com!
Чтобы существовал треугольник, должно быть отмечено три точки. Полученный треугольник будет единственным.
Можно отметить четыре точки, которые расположены в вершинах квадрата. Эти точки находятся на окружности, для которой диагонали квадрата являются диаметрами. При этом получаются четыре прямоугольных треугольника. По-другому отметить четыре точки невозможно, потому что из любой точки, не совпадающей с вершиной квадрата, сторона квадрата видна не под прямым углом. По этой же причине невозможно отметить больше четырёх точек.
Чтобы существовал треугольник, должно быть отмечено три точки. Полученный треугольник будет единственным.
Можно отметить четыре точки, которые расположены в вершинах квадрата. Эти точки находятся на окружности, для которой диагонали квадрата являются диаметрами. При этом получаются четыре прямоугольных треугольника. По-другому отметить четыре точки невозможно, потому что из любой точки, не совпадающей с вершиной квадрата, сторона квадрата видна не под прямым углом. По этой же причине невозможно отметить больше четырёх точек.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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