If the sum of the circumferences of a finite number of convex domains is smaller than the circumference of the convex envelope, then there is a straight line who is separating the convex domains.
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A circle covering theorem. Amer. Math. Monthly52, 494–498 (1945).
W. Blaschke, Vorlesungen über Integralgeometrie, 1. Heft, B. G. Teubner, Leipzig und Berlin 1936, S. 11, Formel (60).