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segment divides square in 2 tangential polygons, find length in terms of inradii

Source: Sharygin 2006 VIII-IX CR 8

August 23, 2019
geometrysquareSegmenttangential quadrilateralinradius

Problem Statement

The segment ABAB divides the square into two parts, in each of which a circle can be inscribed. The radii of these circles are equal to r1r_1 and r2r_2 respectively, where r1>r2r_1> r_2. Find the length of ABAB.
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