You may also like

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?

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?

Symmetric Trace

Points off a rolling wheel make traces. What makes those traces have symmetry?

Roaming Rhombus

Age 14 to 16 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.