Another method - starting with the regular "inscribed" polygon, you can select it and use Transform/Scale to turn it into a "circumscribed" style by doing this.

First point of the scale at the center:



Second point of scale at the midpoint of an edge:



Third point of scale at the endpoint of an edge:



That adjusts the size of the polygon by the exact amount to turn it from an inscribed style to a circumscribed style around the same circle.

- Michael