Предмет: Геометрия, автор: dimagontarenkotar

в окружности проведены хорды AK и BM которые пересекаются в точке С найдите длину отрезка KM если ab=4см,bc=2 см,kc=8см

Ответы

Автор ответа: PhysM

0

Воспользуемся следующим свойством пересекающихся хорд:
$KCcdot AC=BCcdot CM\cfrac{BC}{KC}=cfrac{AC}{CM}$
Треугольник ВАС подобен треугольнику КСМ, по двум сторонам и углу:
1) Угол ВСА = углу КСМ ( вертикальные)
Из свойства хорд получили:
$cfrac{BC}{KC}=cfrac{AC}{CM}$
Получаем, что треугольник ВСА подобен треугольнику КСМ.
Находим КМ:
$cfrac{KM}{AB}=cfrac{KC}{BC}=4\KM=4AB=16$
Ответ: 16 см

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