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Compare Areas

Age 14 to 16 Challenge Level:

Why do this problem ?


This problem brings together ideas of areas of circles and squares, the use of Pythagoras' Theorem and the property of tangents to a circle from an exernal point.

Possible approach


This printable worksheet may be useful: Compare Areas.

You might start with the middle diagram which is the easiest. It brings in the ratio of the sides of an isosceles right angles triangle which is again used in the other two parts.

Key questions


If you know the side length of an isosceles right angled triangle how do you find the hypotenuse?

Which lengths are equal in the diagram?

Which angles are equal?

Can you use the symmetry of the diagram?