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Консультация № 110330
20.11.2007, 22:15
0.00 руб.
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Даны вершины треугольника а=(-1,-1) ;b= (1,-3);c= (2,4)
найти центр описанной окружности и ее радиус. вычисления не надо только формулы
найти центр описанной окружности и ее радиус. вычисления не надо только формулы
Обсуждение
Неизвестный
20.11.2007, 22:54
общий
это ответ
Здравствуйте, lyalya!
Пусть O(x;y) — центр описанной окружности. Тогда
|OA| = |OB| = |OC| = R, (*)
или
|OA|² = |OB|² = |OC|² = R².
|OA|² = (x+1)² + (y+1)²,
|OB|² = (x-1)² + (y+3)², (**)
|OC|² = (x-2)² + (y-4)².
Составляете систему из трёх уравнений:
(x+1)² + (y+1)² = (x-1)² + (y+3)²,
(x+1)² + (y+1)² = (x-2)² + (y-4)²,
(x-1)² + (y+3)² = (x-2)² + (y-4)².
Решением этой системы будут координаты искомого центра описанной окружности. Радиус вычислите с помощью формул (*) и (**).
Пусть O(x;y) — центр описанной окружности. Тогда
|OA| = |OB| = |OC| = R, (*)
или
|OA|² = |OB|² = |OC|² = R².
|OA|² = (x+1)² + (y+1)²,
|OB|² = (x-1)² + (y+3)², (**)
|OC|² = (x-2)² + (y-4)².
Составляете систему из трёх уравнений:
(x+1)² + (y+1)² = (x-1)² + (y+3)²,
(x+1)² + (y+1)² = (x-2)² + (y-4)²,
(x-1)² + (y+3)² = (x-2)² + (y-4)².
Решением этой системы будут координаты искомого центра описанной окружности. Радиус вычислите с помощью формул (*) и (**).
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