Transversals for Families of Translates of a Two-Dimensional Convex Compact Set

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. Received December 28, 1998, and in revised form October 20, 1999. Online publication May 15, 2000.