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<BAO, < CBO, < ACO >= 30^o, O interior of ABC => ABC equilateral

Source: Germany 2000 p3

February 23, 2020
Equilateralanglesgeometry

Problem Statement

Suppose that an interior point OO of a triangle ABCABC is such that the angles ∠BAO,∠CBO,∠ACO\angle BAO,\angle CBO, \angle ACO are all greater than or equal to 30o30^o. Prove that the triangle ABCABC is equilateral.
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