Предмет: Геометрия, автор: KamilaMin2007

ПОМОГИТЕ ПОЖАЛУЙСТА!! СРОЧНО!

Через точку М, лежащую на хорде AB, проходит радиус окружности и делится точкой M на отрезки в отношении 3:1, считая от центра окружности. Найдите радиус окружности если АМ-7 см и МВ=1 см.

siestarjoki: Если хорды делятся точкой пересечения в равном отношении, то они равны (следует из т о пересекающихся хордах). Точка M делит радиус 3:1, а диаметр 7:1. Тогда хорда AB и есть диаметр и радиус равен 4.

Ответы

Автор ответа: liftec74

2

Ответ: 4 cm

Объяснение:

Пусть радиус окружности (О - центр окружности) ОР делится на отрезки ОМ=3х и МР=х. Тогда радиус ОР=4х

Тогда диаметр окружности PТ равен 8х => TM=7x MP=x

Тогда согласно теоремы о пересекающихся хордах имеем:

AM*MB=TM*MP=> 7*1=7x*x 7x²=7 x²=1 x=1 => r=OP=4x=4 cm

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