A convex planar domain in which the minimal generalized diameter is 
always contains a circle of radius
1/3.
Blaschke's Theorem
See also
Generalized DiameterExplore with Wolfram|Alpha
References
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 25, 1983.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 17-18, 1991.Referenced on Wolfram|Alpha
Blaschke's TheoremCite this as:
Weisstein, Eric W. "Blaschke's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BlaschkesTheorem.html