Let a circle of radius b roll, without slipping, inside a fixed circle of radius a. a

Question:

Let a circle of radius b roll, without slipping, inside a fixed circle of radius a. a > b. A point P on the rolling circle traces out a curve called a hypocycloid. Find parametric equations of the hypocycloid. Place the origin 0 of Cartesian coordinates at the center of the fixed, larger circle, and let the point A(a, 0) be one position of the tracing point P. Denote by B the moving point of tangency of the two circles, and let t, the radian measure of the angle A0B, be the parameter Figure 11.