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Need help to solve this problem.

There are many symmetrical parts in the picture. You can establish relationship among the radii and several other line segments by applying symmetry. If you consider the radius of the smaller circle(s) "x" and the radius of the larger circle(s) "y", can you develop an equation between them? And then why don't you connect the centers and a point of tangent to see whether a right triangle can be formed in order to apply the Pythagorean theorem involving x & y?

* By the way, description/language of the problem should have been a little more elaborate and clarified.

A different point of view, one can also use Descartes' theorem.

https://en.wikipedia.org/wiki/Descartes'_theorem

Hint:construct an isosceles triangle by joining the center of any small circle with the two big circles, then form an equation,solve it.......