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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