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Acute-angled or obtuse-angled triangles in regular 2008-gon

Source: Sharygin contest. The final raund. 2008. Grade 8. Second day. Problem 6

August 31, 2008
geometry unsolvedgeometry

Problem Statement

(B.Frenkin) Consider the triangles such that all their vertices are vertices of a given regular 2008-gon. What triangles are more numerous among them: acute-angled or obtuse-angled?