The circumradius of planar reduced convex bodies

In this paper, we discuss the circumradius of reduced convex polygons and Reuleaux polygons. We prove that from amongst all reduced convex n-gons of a fixed thickness, only the regular n-gon has the minimal circumradius. For Reuleaux polygons, we show that from amongst all n -th Reuleaux polygons, only the regular n -th Reuleaux polygon has the minimal circumradius.