2009年$$AMC10$$竞赛$$A$$第$$19$$题  Circle $$A$$ has radius $$100$$. Circle $$B$$ has an integer radius $$r\textless{} 100$$ 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 $$B\textquotesingle\rm s$$ trip. How many possible values can $$r$$ have?  圆 $$A$$ 的半径为 $$100$$。 圆 $$B$$ 有一个整数半径 $$r\textless{} 100$$ 并且在它绕圆 $$A$$ 的圆周滚动一次时保持与圆 $$A$$ 内切。 这两个圆在圆 $$B$$ 轨迹的起点和终点具有相同的切点。 $$r$$ 可以有多少个可能的值？
选项为:A:$$4$$  B:$$8$$  C:$$9$$  D:$$50$$  E:$$90$$  请回答其中一个选项.