Let three similar isosceles triangles Δ A' B C, Δ A B' C, and Δ A B C' be constructed on the sides of a triangle Δ A B C. Then Δ A B C and Δ A' B' C' are perspective triangles, and the envelope of their perspectrix as the vertex angle of the erected triangles is varied is a parabola known as the Kiepert parabola. It has trilinear conic function x:y:z = a(b^2 - c^2):b(c^2 - a^2):c(a^2 - b^2). This parabola was first studied by Artzt.

Brianchon point | envelope | Euler line | isosceles triangle | Kiepert hyperbola | Lemoine axis | parabola | Parry circle | Parry point | Steiner points | Steiner triangle