A circle or radius R rolls around the inside of a circle of radius 2R, what is the path traced out by a point on its circumference?
Solution
The the rolling circle have center O' and the large circle have center O. Suppose the initial point of contact is A. Let A' be the point of the rolling circle that is initially at A. When the contact has moved to B, take ∠AOB = θ. Then since the small circle has half the radius, ∠A'OB = 2θ. Hence ∠O'OA' = θ, so A' lies on OA. Equally it is clear that it can reach any point on the diameter AC.
© John Scholes
jscholes@kalva.demon.co.uk
1 Nov 2003
Last corrected/updated 1 Nov 03