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Just Rolling Round

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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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Giant Holly Leaf

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).

Rolling Coins

Stage: 4 Challenge Level: Challenge Level:1

    A blue coin rolls round two yellow coins which touch. The coins are the same size.

    coins rolling

    How many revolutions does the blue coin make when it rolls all the way round the yellow coins?

    Investigate for a line of 'n' coins