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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/cms/ together with a good help manual and Quickstart for beginners.