### 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?

### 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?

# Just Rolling Round

##### Age 14 to 16Challenge Level

 Created with GeoGebra The smaller circle, radius $r$, rolls around without slipping inside the circumference of the larger circle, radius $2r$. $P$ is a point on the circumference of the smaller circle . What is the locus of $P$?

NOTES AND BACKGROUND

This dynamic image is drawn using Geogebra, free software and very easy to use. You can download your own copy of Geogebra from http://www.geogebra.org.