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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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Center Path

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of the point X and prove your assertion.

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Rolling Coins

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

Roaming Rhombus

Stage: 4 Challenge Level: Challenge Level:1

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)