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?
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Problem



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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

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