a line intersects all segments
Source: 2020 Simon Marais Mathematics Competition A1
November 17, 2020
combinatoricscombinatorial geometry
Problem Statement
There are points in the plane such that no three are collinear. The points are joined by line segments such that each point is an endpoint of exactly two of the line segments.Prove that there does not exist a straight line in the plane that intersects each of the segments in an interior point.An interior point of a line segment is a point of the line segment that is not one of the two endpoints.