Intersecting segments
Source: 239 MO 2024 J2
May 22, 2024
combinatoricscombinatorial geometry
Problem Statement
There are points on the plane, no three of which lie on the same line. Some segments are drawn between them so that they do not intersect at internal points and any segment with ends among the given points intersects some of the drawn segments at an internal point. Is it true that it is always possible to choose drawn segments having no common ends?