Claims

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1945_11_01_goodman_goodman: Finitely many disks in the plane that no disjoint line separates lie in one disk whose radius is the sum of their radii; the 1945 refereed proof of Erdős's conjecture, credited by the site, with a Lean formalization linked.

1947_12_01_hadwiger: For a nonseparable system of plane convex curves, the perimeter, diameter and circumradius of its convex hull are at most the sums of those of its members; the circumradius inequality contains the circle covering theorem.

2015_07_17_bezdek_litvak: Theorem 6.1 of Packing convex bodies by cylinders bounds the circumradius of the hull of nonseparable disks by the sum of their radii through an integral-geometric lemma; a second proof of the circle covering theorem.

2016_02_02_bezdek_langi: A nonseparable family of positive homothets of an o-symmetric convex body with ratios tau_i is covered by a translate of the body scaled by their sum; for the disk this is the circle covering theorem.

2016_05_13_akopyan_balitskiy_grigorev: A nonseparable family of positive homothets of a convex body K is covered by a translate of (sigma+1)/2 times the sum of the ratios times K, with sigma the asymmetry of K; sigma = 1 for the disk gives the circle covering theorem.

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