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.

2D shapes and their properties. Generalising. Circle properties and circle theorems. Making and proving conjectures. Area - circles, sectors and segments. Pythagoras' theorem. Creating and manipulating expressions and formulae. Inequalities. Mathematical reasoning & proof. Regular polygons and circles.