Then why use the word “inscribe” and show the small red circle inscribed in your image?
to draw within a figure so as to touch in as many places as possible
a regular polygon inscribed in a circle
calcolo sezione media_2024Aug10a.gh (32.1 KB)
Playing with your ‘Radius’ sliders, I see this doesn’t always work. 
Later, after coffee.
P.S. There are some conditions where the outer circle appears to be impossible, and other conditions where it is possible but the CircleTTT ‘P’ input (guide point) is wrong.
calcolo sezione media_2024Aug10b.gh (32.4 KB)