Originally Posted by

**mklotz**
And you would have learned exactly no math that would be useful in other applications.

Plus, had you learned some math, you could solve this problem in your head in two seconds...

The distance from the center of a flat to the opposing vertex (dfv) is clearly the sum of the distance from the center to the vertex, the radius (r) of the circumscribed circle, plus the apothem distance to the flat which is r times the cosine of the polygon half angle [360/(2N)].

Thus...

dfv = r * (1 + cos[360/(2N)])

or

r = dfv / (1 + cos[360/(2N)])

and the diameter is twice that.