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segment divides a square in 2 tangential polygons, computational

Source: 2010 IMAC Arhimede P4

May 2, 2019

Segmentgeometryinradiustangential quadrilateral

Problem Statement

Let

M

and

N

be two points on different sides of the square

ABCD

. Suppose that segment

MN

divides the square into two tangential polygons. If

R

and

r

are radii of the circles inscribed in these polygons (

R> r

), calculate the length of the segment

MN

in terms of

R

and

r

.
(Moldova)