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H3 : a^2 (v + w) / (v - w) = 0 (1)

aH3 : a^2 u / (v - w) = 0 (2)

meaning that the line u x + v y + w z = 0 is tangent to the curve. Note that (1) is the barycentric equation of K010 which is the dual of H3. See also K244.

on H3 : X(1553), X(6070), X(6071), X(6072), X(6073), X(6074), X(6075), X(6076), X(6077), X(14499) up to X(14507), vertices of the cevian triangle of X(69)

on aH3 : X(14480), X(14508) up to X(14515), vertices of the circumtangential triangle

The Steiner deltoid H3 (envelope of Simson lines) and its anticomplement aH3 (envelope of axis of inscribed parabolas) are two very famous curves in triangle geometry.

There's no question of reconsidering here their very numerous properties. We will only point out their connection with some cubics or other curves.

cubic

notes

K071

contains the cusps of H3, a stelloid

K077

contains the cusps of aH3, a stelloid

K244

contains the cusps of H3 and those of any deltoid inscribed in ABC, an acnodal cubic

K412

contains the contacts of H3 with the nine point circle, an equilateral cubic

K583

contains the contacts of the deltoids above with their incircle, a nodal cubic

K648

contains the cusps of H3, a circular cubic

K649

contains the cusps of H3,

K650

contains the cusps of H3,

K651

contains the cusps of H3,

K652

contains the cusps of H3,

K722

contains the contacts of H3 with the nine point circle, an acnodal cubic

K723

contains the contacts of aH3 with the circumcircle, an acnodal cubic

 

 

Q046

related with bipedal and bicevian ellipses tritangent to H3