I was working out some old putnam problems and one of them is as follows: "A circle radius r rolls around the inside of a circle radius 3r, so that a point on its circumference traces out a curvilinear triangle. Find the area inside this figure." Currently I'm just trying to find the equation of the path it traces. According to the following site: http://www.kalva.demon.co.uk/putnam/psoln/psol396.html it is not hard to see that x/r = 3 - 2 cos θ - cos 2θ, y/r = 2 sin θ - sin 2θ. But I can't see it. Can anybody help explain why this is so?