Problem

Source: Sharygin 2006 VIII-IX CR 8

Tags: geometry, square, Segment, tangential quadrilateral, inradius



The segment $AB$ divides the square into two parts, in each of which a circle can be inscribed. The radii of these circles are equal to $r_1$ and $r_2$ respectively, where $r_1> r_2$. Find the length of $AB$.