Предмет: Геометрия, автор: Johnny1998

Диалональ равнобедренной трапеции перпендикулярна к боковой стороне а угол между боковой стороной и большей основы трапеции равняеться а.Найдите радиус круга вписаного вокруг трапеции если ее высота равняеться h

Ответы

Автор ответа: Aleksandrela

нам дана трапеция ABCD в которой угол между диагональю и боковой стороной равен 90. (ABD=90)

мы будем решать задачу отталкиваясь от треугольника ABD, который также является вписанным в окружность

известно что если треугольник прямоугольный то радиус описанной окружности лежит на середине гипотенузы и равен половине гипотенузы

значит нм и надо ее найти

она равна AD= $sqrt{AB^2+BD^2}$

AB=h/sina BD=tga*AB=tga*h/sina=h/cosa

отсюда $AD=sqrt{(h/sina)^2+(h/cosa)^2}$

ну и радиус соответственно R= $AD/2=frac{sqrt{(h/sina)^2+(h/cosa)^2}}{2}$

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