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Find the length as a function of r_1 and r_2

Source:

September 22, 2010

geometrylengthscirclesLocus problemsIMO Shortlist

Problem Statement

We are given two mutually tangent circles in the plane, with radii

r_1, r_2

. A line intersects these circles in four points, determining three segments of equal length. Find this length as a function of

r_1

and

r_2

and the condition for the solvability of the problem.