IMO 1988 LL POL70

In 3-dimensional space a point O is given and a finite set A

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IMO 1988 LL POL70

Origin: POL

Problem

In 3-dimensional space a point O is given and a finite set A of segments with the sum of the lengths equal to 1988. Prove that there exists a plane disjoint from A such that the distance from it to O does not exceed 574.