T. Vickers, Equilateral Jacobi
Forum Geometricorum, 17 (2017) 101--113.
Abstract. Given any triangle and any three angles (α, β, γ), the Jacobi construction produces a triangle (here chosen to be equilateral) in perspective with the first. For scalene triangles there are a finite number of values of β, γ for which two values of α give equilateral triangles. The construction of Morley has this property but so do certain other configurations.
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