M2790

Part of Kvant 2024

Problems(1)

Three of 9 vertics of nonagon form obtuse triangle

Source: Kvant M2790 and 45th ToT

Prove that among the vertices of any convex nonagon, three can be found forming an obtuse triangle, none of whose sides coincide with the sides of the nonagon. Proposed by A. Yuran

geometrycombinatorics