Question

Диагональ равнобедренной трапеции перпендикулярна боковой стороне. Найдите радиус окружности, описанной около трапеции, если диагональ равна 12 см, а боковая сторона-9см

Answer 1

Большее основание будет диаметром трапеции, вписанный прямой угол всегда опирается на диаметр. При катетах 9 и 12 гипотенуза (то есть большое основание трапеции)  равна 15, поэтому радиус окружности 7,5

Answer 2

Finding the Radius of the Circumscribed Circle of an Isosceles Trapezoid

To find the radius of the circle circumscribed around an isosceles trapezoid, we need to use the given information about the trapezoid's diagonal and one of its side lengths.

Let's denote the diagonal of the trapezoid as d (given as 12 cm) and one of its side lengths as a (given as 9 cm).

To find the radius of the circumscribed circle, we can use the formula:

radius = (1/2) * √(d^2 - 4a^2)

Substituting the given values into the formula, we get:

radius = (1/2) * √((12 cm)^2 - 4(9 cm)^2)

Simplifying the equation:

radius = (1/2) * √(144 cm^2 - 4 * 81 cm^2) radius = (1/2) * √(144 cm^2 - 324 cm^2) radius = (1/2) * √(-180 cm^2)

Since the result is a negative value, it indicates that the given dimensions do not form a valid isosceles trapezoid. Please double-check the provided values for the diagonal and side length.

If you have any further questions, feel free to ask!