You may also like

problem icon

Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

problem icon

Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

problem icon

Cube Paths

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

The Pillar of Chios

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
rectangles and crescents

Semicircles are drawn on the sides of a rectangle ABCD as shown in the diagram. A circle passing through points ABCD carves out four crescent-shaped regions (coloured yellow and green in the diagram).

Prove that the sum of the areas of the four crescents is equal in area to the rectangle ABCD.