Question

Найдите радиус окружности, описанной около треугольника со сторонами 9,10,17?

Answer 1

p = P/2 = (9+10+17)/2 = 18
Найдем площадь по формуле Герона   S = √(р (р-а) (р-в) (р-с) , р-полупериметр
√(18 (18 - 9) (18 - 10) (18 - 17)) = √(18 * 9 * 8 * 1) = 36
R=a*b*c/4S   R = 9 * 10 * 17 / (4 * 36) = 10,625

Answer 2

Finding the Radius of the Circumscribed Circle

To find the radius of the circle circumscribed around a triangle with side lengths 9, 10, and 17, we can use the following formula:

Radius of the circumscribed circle = (abc) / (4A)

Where: - a, b, and c are the side lengths of the triangle - A is the area of the triangle

Let's calculate the radius using this formula.

First, we need to calculate the area of the triangle. We can use Heron's formula to find the area:

A = sqrt(s(s-a)(s-b)(s-c))

Where: - s is the semiperimeter of the triangle, calculated as (a + b + c) / 2

Let's calculate the area and the radius using the given side lengths.

Using the side lengths 9, 10, and 17, we can calculate the semiperimeter:

s = (9 + 10 + 17) / 2 = 18

Now, let's calculate the area of the triangle using Heron's formula:

A = sqrt(18(18-9)(18-10)(18-17)) = sqrt(18 * 9 * 8 * 1) = sqrt(1296) = 36

Now that we have the area of the triangle, we can calculate the radius of the circumscribed circle:

Radius = (9 * 10 * 17) / (4 * 36) = 1530 / 144 = 10.625

Therefore, the radius of the circle circumscribed around the triangle with side lengths 9, 10, and 17 is approximately 10.625.

Answer

The radius of the circle circumscribed around the triangle with side lengths 9, 10, and 17 is approximately 10.625.