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The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

Six Discs

Age 14 to 16
Challenge Level

What would happen if you superimposed B on A? What about D on E?

Diagram B
These diagrams show some right-angled triangles you can use to work out the lengths on shapes B and D using trigonometry. What angles do you know? What sides do you know?