AMC 10A 2009 Problem 19

Circle A has radius 100 . Circle B has an integer radius r<100 and remains internally tangent to circle A as it rolls once around the circumference of circle A. The two circles have the same points of tangency at the beginning and end of circle B 's trip. How many possible values can r have?

Answer Choices
A. 4
B. 8
C. 9
D. 50
E. 90