The Steiner triangle Δ S_A S_B S_C (a term coined here for the first time), is the Cevian triangle of the Steiner point S. It is the polar triangle of the Kiepert parabola. It has the trilinear vertex matrix [0 | (b^2 - a^2) c | b(a^2 - c^2) (b^2 - a^2) c | 0 | a(c^2 - b^2) b(c^2 - a^2) | a(b^2 - c^2) | 0]. The vertices are the points of contact of the Kiepert parabola with the sidelines of the reference triangle.

Kiepert parabola | second Steiner circle | Steiner points