MathDB
Every angle in triangle σ is greater than θ in partition

Source: Japanese MO Finals 1996

February 11, 2011
geometrycircumcirclecombinatorics unsolvedcombinatorics

Problem Statement

A plane is partitioned into triangles. Let T0\mathcal{T}_0 denote the set of vertices of triangles in the partition. Let ABCABC be a triangle with A,B,C∈T0A,B,C\in\mathcal{T}_0 and θ\theta be its smallest angle. Assume that no point of T0\mathcal{T}_0 lies inside the circumcircle of △ABC\triangle ABC. Prove that there exists a triangle σ\sigma in the partition such that its intersection with △ABC\triangle ABC is nonempty and whose every angle is greater than θ\theta.
Back to ProblemsView on AoPS