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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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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?

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Either Side

A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

Roaming Rhombus

Age 14 to 16 Challenge Level:

Four rods of equal lengths are hinged at their endpoints to form a rhombus ABCD.


Keeping AB fixed, CD is free to move in the plane with the angle BAD between 0 and 180 degrees.

What is the locus (or path) of the point D?

What is the locus of Y, the point one third of the way along DC? (DY:YC = 1:2)