IMO 1989 LL POL80

We are given a finite collection of segments in the plane, of

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IMO 1989 LL POL80

Origin: POL

Problem

We are given a finite collection of segments in the plane, of total length 1. Prove that there exists a line ℓsuch that the sum of the lengths of the projections of the given segments to the line ℓis less than 2/\pi.