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exists a plane through O not intersecting any of n segments.

Source: Israel Joseph Gillis Mathematical Olympiad 1998 p1

February 16, 2020
combinatorial geometryPlanegeometryangles

Problem Statement

In space are given nn segments AiBiA_iB_i and a point OO not lying on any segment, such that the sum of the angles AiOBiA_iOB_i is less than 180o180^o . Prove that there exists a plane passing through OO and not intersecting any of the segments.
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