Blas Herrera,
Algebraic Equations of All Involucre Conics in the Configuration of the c-Inscribed Equilateral Triangles of a Triangle,
Forum Geometricorum, 18 (2018) 223--238.

Abstract. Let Δ ABC be a triangle with side length c=AB; here we present the determination of the existence and quantity m of the c-inscribed equilateral triangles {Tⱼ}_{j=1}^{j=m} (i.e.  Tⱼ = Δ AⱼBⱼCⱼ with Aⱼ in BC, Bⱼ in CA, Cⱼ in AB, c = AⱼBⱼ ) of Δ ABC in function of the position of vertex C respect to a separatrix parabola Pᵢ, and from an algebraic point of view. We give the algebraic equations of all involucre conics --circles Nₒ, Nᵢ; parabola Pᵢ; ellipses Hᵢ, Hₒ -- in the configuration.

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