P is a point on the circumference of a circle radius r, which touches another circle radius 2 r, from the inside.

The smaller circle rolls, without slipping, around the circumference of the larger circle.

What is the locus of P?

A dynamic version of this problem is available below if you have a Java-enabled browser.

The smaller circle can be moved inside the larger circle by dragging the red point. The Show and Hide buttons allow you to view the locus of the blue point.