**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 {**T**ⱼ}_{j=1}^{j=m} (i.e. **T**ⱼ = 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 *P*ᵢ, 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.

[ps
file] [pdf]

Return to Forum
Geom., 18 (2018) Table of Contents