6 collinear point, triangle ineq. May Olympiad (Olimpiada de Mayo) 2012 L2 P4
Source:
September 29, 2021
combinatorial geometrycombinatoricstriangle inequality
Problem Statement
Six points are given so that there are not three on the same line and that the lengths of the segments determined by these points are all different. We consider all the triangles that they have their vertices at these points. Show that there is a segment that is both the shortest side of one of those triangles and the longest side of another.