Question

очень срочно. радиус окружности вписанной в квадрат равен 10 корней из 2. найдитье радиус окружности описанной около этого квадрата

Answer 1

диаметр описанной окружности равен диагонали квадрата, а диаметр вписанной равен стороне квадрата, значит сторона квадрата =20 корней из 2, дальше по теореме Пифагора находим диаметр описанной  окружности                получается 40, делим пополам получается радиус описанной окружности около этого квадрата равен 20                                                                                                                                                    

Answer 2

Radius of the Inscribed Circle

To find the radius of the circle inscribed in a square, we can use the given information that the radius of the inscribed circle is equal to 10√2.

Radius of the Circumscribed Circle

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

In a square, the diagonal is equal to twice the radius of the circumscribed circle. Therefore, we can use the formula:

Diagonal of the Square = 2 * Radius of the Circumscribed Circle

Since the diagonal of the square is equal to the side length of the square multiplied by √2, we can write:

Side Length of the Square * √2 = 2 * Radius of the Circumscribed Circle

Substituting the given value of the side length of the square as 10√2, we can solve for the radius of the circumscribed circle:

10√2 * √2 = 2 * Radius of the Circumscribed Circle

Simplifying the equation:

20 = 2 * Radius of the Circumscribed Circle

Dividing both sides by 2:

10 = Radius of the Circumscribed Circle

Therefore, the radius of the circle circumscribed around the given square is 10.

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