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Answering a question of Füredi and Loeb [On the best constant for the Besicovitch covering theorem.  Proc. Amer. Math. Soc.   121 (4) (1994), 1063–1073], we show that the maximum number of pairwise intersecting homothets of a   d  ‐dimensional centrally symmetric convex body   K  , none of which contains the center of another in its interior, is at most    O  (   3  d   d   log       d  )   . If   K   is not necessarily centrally symmetric and the role of its center is played by its centroid, then the above bound can be replaced by    O  (   3  d2  d   d    d   log       d  )   . We establish analogous results for the case where the center is defined as an arbitrary point in the interior of   K  . We also show that, in the latter case, one can always find families of at least    Ω  (    (  2  /   3   )   d   )    translates of   K   with the above property.

ARRANGEMENTS OF HOMOTHETS OF A CONVEX BODY