Question

Квадрат описано навколо кола радіуса 3см. Знайдіть радіус кола, описаного навколо квадрата

Answer 1

r=a/2

a=2r

a = 2*3 = 6(см)

R=a/корiнь 2

R=3 корінь 2

Answer 2

Problem Statement

We are given a square inscribed in a circle with a radius of 3 cm. We need to find the radius of the circle circumscribed around the square.

Solution

To find the radius of the circle circumscribed around the square, we can use the relationship between the diagonal of the square and the radius of the circle.

Let's assume the side length of the square is 's' and the radius of the circle is 'R'.

The diagonal of the square is equal to twice the radius of the circle, so we have:

Diagonal of the square = 2 * R

The diagonal of the square can be calculated using the Pythagorean theorem, where the diagonal is the hypotenuse of a right triangle with the sides equal to the side length of the square:

Diagonal of the square = s * sqrt(2)

Setting these two equations equal to each other, we can solve for the radius of the circle:

s * sqrt(2) = 2 * R

Simplifying the equation, we get:

R = (s * sqrt(2)) / 2

Now, let's substitute the value of the side length of the square. Since the square is inscribed in the circle, the diagonal of the square is equal to the diameter of the circle. The diameter is twice the radius, so the diagonal of the square is equal to 2 * 3 cm = 6 cm.

s = 6 cm

Substituting this value into the equation, we can calculate the radius of the circle:

R = (6 cm * sqrt(2)) / 2

Calculating this expression, we find:

R ≈ 4.24 cm

Therefore, the radius of the circle circumscribed around the square is approximately 4.24 cm.

Answer

The radius of the circle circumscribed around the square is approximately 4.24 cm.