  Let $M$ be a $2$-space form. Let $P$ be a convex polygon in $M$. For these
polygons, we define (and justify) a curvature $\kappa_i$ at each vertex $A_i$
of the polygon and and prove the following Blaschke's type theorem: If $P$ is a
convex plygon in $M$ with curvature at its vertices $\kappa_i\ge \kappa_0 >0$,
then the circumradius $R$ of $P$ satisfies $ta_\lambda(R) \le \pi/(2\kappa_0)$
and the equality holds if and only if the polygon is a $2$-covered segment.
