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Coke Machine

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

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At a Glance

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

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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.

Swings and Roundabouts

Age 14 to 16 Challenge Level:
It is important first to establish the principle of moments via the easier problem "Inside Outside".

Then use some reasoning about angles and trigonometry to solve this problem.