The following construction is used for training astronauts:
A circle C2 of radius 2R rolls along the inside of another, fixed circle C1 of radius nR, where n is an integer greater than 2. The astronaut is fastened to a third circle C3 of radius R which rolls along the inside of circle C2 in such a way that the touching point of the circles C2 and C3 remains at maximum distance from the touching point of the circles C1 and C2 at all times. How many revolutions (relative to the ground) does the astronaut perform together with the circle C3 while the circle C2 completes one full lap around the inside of circle C1? geometry proposedgeometry