We are given two mutually tangent circles in the plane, with radii
![r_1, r_2](/media/m/f/9/e/f9eac5f394e6f354c825a61d197c1b14.png)
. A line intersects these circles in four points, determining three segments of equal length. Find this length as a function of
![r_1](/media/m/9/0/1/901ecb943995b3585cd44466e1b750cb.png)
and
![r_2](/media/m/9/0/6/90608ee2be6d3b5c7f96a6ca45780ec4.png)
and the condition for the solvability of the problem.
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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.