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.

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