Предмет: Геометрия, автор: cyborgcat

Помогите пожалуйста, если можно с рисунком

1)В треугольнике ABC AD и CE-высоты, ∠ACB=28°. Найдите ∠CBO.

2)В треугольнике ABC медианы BB_1 и СС_1 пересекаются в точке О и равны 15 см и 18 см соответственно. Найдите периметр треугольника ABC, если ∠BOC=90°.

3)В треугольнике ABC биссектрисы BB1 и AA1 пересекаются в точке О. Найдите отношение площадей треугольников AOC и BOC, если AC=8 см, BC=6 см.

Ответы

Автор ответа: atavinaekaterina176

1

Ответ:

1) Высоты треугольника пересекаются в одной точке. Значит, высота BF проходит через O. Треугольник CBF прямоугольный, один острый угол равен 28, а второй нужно найти (прямая BO совпадает с прямой BF, нам достаточно найти угол CBF). Тогда второй острый угол равен 90-28=62.

2)Так как СС1 и ВВ1 медианы треугольника, то точка О делит их в отношении 2 / 1 начиная с вершины.

Тогда ОС = 2 * СС1 / 3 = 2 * 18 / 3 = 12 см, ОС1 = СС1 / 3 = 6 см.

ОВ = 2 * ВВ1 / 3 = 2 * 15 / 3 = 10 см, ОВ1 = ВВ1 / 3 = 5 см.

Так как СС1 перпендикулярно ВВ1, то в прямоугольном треугольнике ВОС по теореме Пифагора, ВС2 = ОС2 + ОВ2 = 144 + 100 = 244.

ВС = √136 = 2 * √61 см.

СВ12 = ОС2 + ОВ12 = 144 + 25 = 169.

СВ1 = 13 см, тогда АС = 2 * СВ1 = 2 * 13 = 26 см.

ВС12 = ОВ2 + ОС12 = 100 + 36 = 136.

ВС1 = 2 * √34 см, тогда АВ = 4 * √34 см.

Тогда периметр треугольника АВС равен:

Равс = 2 * √61 + 4 * √34 + 13 см.

Ответ: Периметр равен 2 * √61 + 4 * √34 + 13 см.

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