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P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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Coke Machine

Age 14 to 16
Challenge Level

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

Coins inserted into the machine slide down a chute into the machine and a drink is duly released.

How many more revolutions does the foreign coin make over the 50 pence piece going down the chute?