Question

1.найдите радиус окружности, описанной около прямоугольника, две стороны которого равны 27 и корень из 295 2.Найдите диагональ прямоугольника вписанного в окружность радиус которой равен 2 корень из 2. 3.Найдите радиус окружности описанной около прямоугольника две стороны которого равны 11 и корень из 135

Answer 1

В 1 и 3 задаче найди диагональ по теореме Пифагора и раздели её на двое будет радиус Во второй задаче радус умножал на два будет диагональ

Answer 2

Question translation: Answer in detail. 1. Find the radius of the circle circumscribed around a rectangle, two sides of which are equal to 27 and the square root of 295. 2. Find the diagonal of the rectangle inscribed in a circle with a radius of 2 times the square root of 2. 3. Find the radius of the circle circumscribed around a rectangle, two sides of which are equal to 11 and the square root of 135.

To find the radius of the circle circumscribed around a rectangle, we can use the Pythagorean theorem. Let's solve each question step by step.

1. Find the radius of the circle circumscribed around a rectangle with sides 27 and the square root of 295.

To find the radius, we need to determine the diagonal of the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the two sides.

Let's denote the sides of the rectangle as length (L) and width (W). In this case, L = 27 and W = sqrt(295).

Using the Pythagorean theorem, we can find the diagonal (D) of the rectangle:

D^2 = L^2 + W^2

Substituting the values, we have:

D^2 = 27^2 + (sqrt(295))^2

Simplifying the equation:

D^2 = 729 + 295

D^2 = 1024

Taking the square root of both sides:

D = sqrt(1024)

D = 32

The diagonal of the rectangle is 32. Since the diagonal is also the diameter of the circumscribed circle, the radius is half of the diameter:

Radius = D/2 = 32/2 = 16

Therefore, the radius of the circle circumscribed around the rectangle is 16.

2. Find the diagonal of the rectangle inscribed in a circle with a radius of 2 times the square root of 2.

To find the diagonal of the rectangle, we can use the relationship between the radius of the inscribed circle and the diagonal of the rectangle. The diagonal is equal to twice the radius of the inscribed circle.

Let's denote the radius of the inscribed circle as R. In this case, R = 2 * sqrt(2).

The diagonal (D) of the rectangle is equal to 2R:

D = 2 * R = 2 * (2 * sqrt(2)) = 4 * sqrt(2)

Therefore, the diagonal of the rectangle inscribed in the circle with a radius of 2 times the square root of 2 is 4 times the square root of 2.

3. Find the radius of the circle circumscribed around a rectangle with sides 11 and the square root of 135.

Similar to the first question, we can find the radius by determining the diagonal of the rectangle using the Pythagorean theorem.

Let's denote the sides of the rectangle as length (L) and width (W). In this case, L = 11 and W = sqrt(135).

Using the Pythagorean theorem, we can find the diagonal (D) of the rectangle:

D^2 = L^2 + W^2

Substituting the values, we have:

D^2 = 11^2 + (sqrt(135))^2

Simplifying the equation:

D^2 = 121 + 135

D^2 = 256

Taking the square root of both sides:

D = sqrt(256)

D = 16

The diagonal of the rectangle is 16. Since the diagonal is also the diameter of the circumscribed circle, the radius is half of the diameter:

Radius = D/2 = 16/2 = 8

Therefore, the radius of the circle circumscribed around the rectangle is 8.