Poblem 1 (jbmo tst), moldova
Source: JBMO TST, Moldova
March 31, 2006
geometry proposedgeometry
Problem Statement
Five segments have lengths such that any three of them can be sides of a - possibly degenerate - triangle. Also, the lengths of these segments are nonzero and pairwisely different. Prove that there exists at least one acute-angled triangle among these triangles.