What is the area of the largest circular rug that will exactly fit in a square room with an area of 144 square feet?

Rectangle ABCD is inscribed in a circle with center X. If the area of the rectangle is eight times its width, and the distance from X to side AB is three, what is the approximate circumference of the circle?

In the circle above with center C, diameter . Which of the following must be true?

I. The length of minor arc BD is greater than .

II. Angle ABD measures .

III. Triangle BCD is equilateral.

Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is , what is the ratio of the area of Square A to the area of Square C?

Square ABCD is perfectly inscribed in the circle pictured above. If minor arc AD measures , what is the approximate area of the shaded region?

A square is inscribed within a circle as shown above. If the area of the square is 32 square inches, what is the area of the circle, in square inches?

Three identical circles, each tangent to the adjacent circle at one point as shown, are perfectly inscribed within a rectangle. If the area of the rectangle is 108 square feet, what is the area, in square feet, of each circle?

A circle of radius is inscribed in a square, as shown in the figure.

What percent of the square’s area is taken up by the circle?

A circle centered on point Z is inscribed within square ABCD as shown above. If the area of square ABCD is 64 square centimeters, what is the area (in square centimeters) of the circle?

A pizza shop wants to determine the dimensions of the smallest square box that will exactly contain its large, circular pizza, which has an area of 225 square centimeters. What is the length of each side of the smallest square box that will exactly contain the pizza?