What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?