# The inner circle

**Geometry**Level 3

Circle #2 is a smaller circle drawn tangent to the \(x\) and \(y\) axes and to circle #1.

Circle #3 is an even smaller circle tangent to the \(x\) and \(y\) axes, and to circle #2.

In general, circle #N is drawn tangent to the \(x\) and \(y\) axes and to circle #(N-1).

**Which decimal is closest to the ratio of the area of circle #101 to the area of circle #100?**