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Relative distance of boundary points of a convex body and touching by homothetical copies

Lángi Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 4

439-444

The relative distance of points p and g of a convex body C is the ratio of the length of the segment pq to the half of the length of a longest chord of C parallel to pq. In this paper we find a connection between pairwise relative distances of k points in the boundary of a convex body and the rafio of k homothetical copies of a convex body touching it.