Предмет: Геометрия, автор: XoOM97

Найдите радиус окружность, если основания описанной около нее равнобедренной трапеции равны 6см и36см

Ответы

Автор ответа: vajny

В описанном 4-нике - суммы противоположных сторон равны. Если с - боковая сторона трапеции, а и b - основания (а = 36, b = 6), то:

а+b = 2с

42= 2с

с = 21

Высота трапеции равна диаметру вписанной окружности.

Опустим из вершин В и С трапеции высоты BK и CM на основание АD= a = 36.

Тогда в прям. тр-ке АВК: АК = (a-b)/2 = 15

По теор. Пифагора:

BK = корень(c^2 - AK^2) = корень(441-225) = корень216 = 6корней6

Тогда радиус:

$r=3sqrt{6} cm.$

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