Triangle of the three centres is obtuse
Source: Romanian TST 1997
September 17, 2011
trigonometryinequalitiesgeometry proposedgeometry
Problem Statement
We are given in the plane a line and three circles with centres such that they are all tangent to and pairwise externally tangent to each other. Prove that the triangle has an obtuse angle and find all possible values of this this angle.Mircea Becheanu