MathDB

1

Part of 1998 Israel National Olympiad

Problems(1)

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

Source: Israel Joseph Gillis Mathematical Olympiad 1998 p1

2/16/2020
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.
combinatorial geometryPlanegeometryangles