circumcircle of every triangle used in triangulation contains entire polygo
Source: 2023 IGO Elementary P5
January 18, 2024
geometrycombinatoricscombinatorial geometrytriangulationconvex polygon
Problem Statement
A polygon is decomposed into triangles by drawing some non-intersecting interior diagonals in such a way that for every pair of triangles of the triangulation sharing a common side, the sum of the angles opposite to this common side is greater than .
a) Prove that this polygon is convex.
b) Prove that the circumcircle of every triangle used in the decomposition contains the entire polygon.Proposed by Morteza Saghafian - Iran