### 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?

### 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.

### 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:

Well done Luke and Daniel from year 9 together with Nicholas and Luke from year 7 of Clevedon Community School who sent in the following solution.

The locus of corner D will be a circle with a radius equal to AD, whose centre is A. The locus of the point Y will be a circle with a radius equal to AD, and a centre on AB one third of the way along from A to B.

Can you see the reason for this? The locus of Y is a circle. If you imagine a line joining Y to the centre Z of this circle then DYZA is a parallelogram so ZY = AD and AZ=DY.