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Sides of quadrangle cannot form triangles

Source: 42nd International Tournament of Towns, Junior A-Level P7, Fall 2020

February 18, 2023
geometryTournament of Towns

Problem Statement

There is a convex quadrangle ABCDABCD such that no three of its sides can form a triangle. Prove that:
[*]one of its angles is not greater than 60∘60^\circ{}; [*]one of its angles is at least 120∘120^\circ.
Maxim Didin
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