So Many Circles

Geometry Level 2

An isosceles right triangle \(ABC\) where \(AB = BC = 5\) and \(\angle ABC = 90 ^ \circ\) is divided into \(25\) congruent right triangles. Each right triangle has an incircle (as shown in the diagram). Find the sum of the radii of all \(25\) incircles. Report your answer to two decimal places.

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