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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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Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

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Triangles and Petals

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Rolling Coins

Age 14 to 16 Challenge Level:

    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