There is a square inscribed in a circle with a radius of 10 cm. Find the area of the square and

There is a square inscribed in a circle with a radius of 10 cm. Find the area of the square and the length of the circle inscribed in this square.

Since ABCD is a square, then AB = BC = CD = AD.

The intersection point of the diagonals of the rectangle coincides with the center of the circle, then the diagonals of the rectangle are equal: AC = BD = 2 * R = 2 * 10 = 20 cm.

From a right-angled triangle ABD, by the Pythagorean theorem, BD ^ 2 = AB ^ 2 + AD ^ 2 = 2 * AB ^ 2.

400 = 2 * AB ^ 2.

AB ^ 2 = 400/2 = 200.

AB = 10 * √2 cm.

Let’s define the area of ​​the square.

Savsd = AB ^ 2 = (10 * √2) 2 = 200 cm2.

The radius of the inscribed circle is half the length of the side of the square.

R = AB / 2 = 10 * √2 / 2 = 5 * √2 cm.

Determine the length of the inscribed circle. L = 2 * n * R = 10 * n * √2 = cm.

Answer: The area of ​​the square is 200 cm2, the circumference is 10 * n * √2 cm.