Distribution of n-set of circles along optimal circumference

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Let's say, there is an arbitrary set of circles with different radiuses.

Have to distribute these circles in this way:

Pretty sure, that first of all need to find R, but don't know how to do it?

UPDATE: Theoretically, this problem could be solved by a simple "brute-force" by setting inner circle radius to smallest one and increasing it step by step while all circles would fit circumference.

But, that's a last resort, hope there is a more elegant way of doing it.

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