The outer Soddy circle is the solution to the four coins problem. It has circle function l = ((-a + b + c)^2[f(a, b, c) + 16g(a, b, c) r s])/(4b c[(a^2 + b^2 + c^2) - 2(a b + b c + c a) + 8r s]^4), where f(a, b, c) and g(a, b, c) are 8th-order and 16th-order polynomials, respectively.
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