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Problems(1)

Find the length as a function of r_1 and r_2

Source:

9/22/2010
We are given two mutually tangent circles in the plane, with radii r1,r2r_1, r_2. A line intersects these circles in four points, determining three segments of equal length. Find this length as a function of r1r_1 and r2r_2 and the condition for the solvability of the problem.
geometrylengthscirclesLocus problemsIMO Shortlist