Q000


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		too complicated to be written here. Click on the link to download a text file.





		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 to bipedal and bicevian ellipses tritangent to H3