# Two semicircles and a quarter of circle are inscribed in the square.What is the correct alternative?

Geometry Level 1

In the diagram below, two semicircles and one quarter-circle are inscribed in a unit square.

Inside one of the partitioned sections, infinitely many circles are drawn that are tangent to each other and to the boundaries. Let $$r_n$$ denote the radius of the $$n^\text{th}$$ largest circle.

Express $$r_n$$ in terms of $$n.$$

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