Find the area of a ring bounded by a circle circumscribed about a square and inscribed in it. Side of the square = 20.

The diameter of the circumscribed circle is equal to the diagonal AC of the square ABCD.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 400 + 400 = 800 cm.

AC = 20 * √2 cm.

Then the radius of the circle is: R = AC / 2 = 20 * √2 / 2 = 10 * √2 cm.

The area of the circle is: S1 = π * R ^ 2 = 200 * π cm2.

The diameter of the inscribed circle is equal to the side of the square, then R = 20/2 = 10 cm.

Then S2 = π * R ^ 2 = 100 * π cm2.

Determine the area of the ring. S = S1 – S2 = 200 * π – 100 * π = 100 * π cm2.

Answer: The area of the ring is 100 * π cm2.