Transversals for Families of Translates of a Two-Dimensional Convex Compact Set
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The following Theorem 1 gives an affirmative answer to Grünbaum's old question. Let F be a family of translates of a convex compact set K⊂R 2 . If every two elements of F have a common point, then there exist three points A, B, C ∈R 2 such that every element of F contains some of these points.