Acute triangle
Source: Spanish 2001; JBMO TST (2006?) Moldova, problem 1; German BWM 1970/71, 1st round, problem 3
February 27, 2006
geometry solvedgeometry
Problem Statement
Given five segments such that any three of them can be used to form a triangle. Show that at least one of these triangles is acute-angled.
Alternative formulation: Five segments have lengths such that any three of them can be sides of a triangle. Prove that there exists at least one acute-angled triangle among these triangles.