Around it, circumscribe an equilateral triangle.
Circumscribe another circle around that.
Circumscribe a square around this circle.
Circumscribe another circle around that.
Circumscribe a regular pentagon around this circle.
Circumscribe another circle around that.
Continue, ad infinitum, with the next regular polygon.
Do the radii of these circles converge? If so, what is the limiting radius?