Предмет: Алгебра, автор: slobaeva

Отрезки AB и DC лежат на параллельных прямых, а отрезки AC и BD
пересекаются в точке M. Найдите MC, если AB=16, DC=24, AC=25

Ответы

Автор ответа: grisha4121

Рассмотрим треугольники ABM и CDM.
∠AMB=∠CMD (т.к. они вертикальные).
∠ABM=∠CDM (т.к. они накрест-лежащие).
Следовательно, треугольники ABM и CDM подобны
AC=AM+MC => AM=AC-MC
Тогда:
AB/CD=AM/MC
16/24=(AC-MC)/MC
16MC=24(25-MC)
2MC=3(25-MC)
2MC=75-3MC
5MC=75
MC=15
Ответ: MC=15

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