ABSTRACT
ABSTRACT. A line l definitely supports a family F of convex bodies in the plane if it supports every member of F and all the bodies are in the same closed half-plane determined by l. F is called k-disjoint, where k(≥2) is a given positive integer, if no k elements of F have a common point. The paper contains new Helly-type results on the existence of a line definitely supporting a k-disjoint family of convex bodies in the plane.
