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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