Problem:
Circle has radius . Circle has an integer radius and remains internally tangent to circle as it rolls once around the circumference of circle . The two circles have the same points of tangency at the beginning and end of circle 's trip. How many possible values can have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Circles and have circumferences and , respectively. After circle begins to roll, its initial point of tangency with circle touches circle again a total of
times. In order for this to be an integer greater than must be one of the integers , or . Hence there are a total of possible values of .
The problems on this page are the property of the MAA's American Mathematics Competitions