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# Just Rolling Round

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### Roaming Rhombus

### Triangles and Petals

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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 $P$? |

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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.

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?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?