17-point cubic | seventeen-point cubic

The Thomson cubic Z(X_2) of a triangle Δ A B C is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot point at the triangle centroid, so its parameter is x = b c and its trilinear equation is given by b c α(β^2 - γ^2) + c a β(γ^2 - α^2) + a b γ(α^2 - β^2) = 0 (Cundy and Parry 1995; Kimberling 1998, p. 240).

triangle cubic