Question

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

Answer 1

Теорема (Соотношение между стороной треугольника, противолежащим углом и радиусом описанной окружности).
сторона делить на синус противолежащего угла = 2 радиуса

синус 90 = 1.Сторону можно найти по теореме пифагора ответ 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 can use the properties of the trapezoid and apply some geometric formulas.

Let's denote the given diagonal as d (which is 12 cm) and the length of the side of the trapezoid as s (which is 9 cm).

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

Radius = (d/2) * √((d/2)^2 + s^2)

Now let's substitute the given values into the formula:

Radius = (12/2) * √((12/2)^2 + 9^2)

Simplifying the equation:

Radius = 6 * √(36 + 81) Radius = 6 * √117 Radius ≈ 6 * 10.82 Radius ≈ 64.92 cm

Therefore, the radius of the circle circumscribed around the given isosceles trapezoid is approximately 64.92 cm.

Please note that the calculations provided are based on the information given in the question and the formulas used in geometry.