# Inspired by toilet paper

Geometry Level 3

Referring to the figure above, suppose $$A_1$$ is area of first white circle, then $$A_2$$ is area of pink annulus, $$A_3$$ is area of blue annulus and like wise $$A_n$$ would be the annulus bounded by $$n^\text{th}$$ and $$(n-1)^\text{th}$$ circle. These $$n$$ concentric circles are drawn such that the area bounded by two concentric circles remains constant, that is $$A_1=A_2=A_3= \cdots = A_n$$.

Define $$r_n$$ to be the radius of $$n^\text{th}$$ circle.Evaluate $$\dfrac{r_{100}}{r_1}$$ correct 2 decimal places.

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