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Radius ratio between the center circle and the others on different polygons like this triangle below.
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We could set the Outer radius (R) to 1
Angle v =JCG is 180*(n-2)/n. The center circle's radius is: (Outer radius R)/cos(v)-R. Is this correct? For example for this triangle. V=180(3-2)/3 = 180/3.
Then to get the inner circle's radius. r = R/cos (V/2)-R = 1/cos (30) - 1. Or somthing so the ratio is 1/6,4. Correct me if you found any mistakes.
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