Question

Найти радиус окружности описанной около квадрата со стороной равной 14√2.

Answer 1

Радиус описанной вокруг квадрата окружности равен половине его диагонали:

R = a*sin45⁰ = 14√2 /√2 = 14

Ответ: 14

Answer 2

радиус окружности равен диагонали квадрата деленной на два.R=14√2*√3/2=14√6/2=7√6

Answer 3

Finding the Radius of the Circle Circumscribed around a Square

To find the radius of the circle circumscribed around a square, we can use the properties of right triangles and trigonometry.

Let's start by considering a square with side length equal to 14√2.

Step 1: Draw the square and the circle circumscribed around it.

Step 2: Draw the diagonal of the square. The diagonal of a square divides it into two congruent right triangles.

Step 3: Let's label the side length of the square as 's' and the radius of the circle as 'r'.

Step 4: The diagonal of the square is equal to the hypotenuse of the right triangle formed by the diagonal and one side of the square. The length of the diagonal can be found using the Pythagorean theorem:

diagonal^2 = side^2 + side^2 diagonal^2 = s^2 + s^2 diagonal^2 = 2s^2

Step 5: Since the diagonal is equal to the diameter of the circle, we can write:

diameter = 2r

Step 6: Equating the diagonal and the diameter, we have:

2s^2 = 2r^2

Step 7: Solving for 'r', we get:

r^2 = s^2 r = s

Therefore, the radius of the circle circumscribed around a square with side length 14√2 is 14√2.

Please note that this answer is based on the properties of a square and the relationship between the side length and the radius of the circumscribed circle. The answer is derived mathematically and does not require external sources for verification.