It is not easy to create concentric circles and quite alot of
work is needed in calculating the diameters of circles based on the
length of the side of your many sided polygon.

A step size of 1 unit and a turn of 1 degree produces a circle
of circumference 360 units.

A step size of 2 units and a turn of 1 degree produces a
circle with a circumference of 720 units.

From these you can work out the diameter as

$C = \pi d$.

That should help you work out where you need to start the next
circle.

Some LOGO programs, like MSWLogo understand "PI" and will do
calculations which include it. For example: PI * 2 will give a
decimal answer.