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K888

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

X(2), X(6), X(23), X(111), X(182), X(184), X(186), X(187), X(353), X(11649)

K888 is a circular cubic invariant under the involution Psi described in the page K018 and in the paper "Orthocorrespondence and Orthopivotal Cubics", ยง5. See also the analogous focal cubic K508. K888 is a Psi-cubic as in Table 60.

Its infinite point S is that of the lines X(23)X(184) and X(182)X(186), SEARCH = 0.940629525009696.

S = a^2 (a^8 b^2-2 a^6 b^4+2 a^2 b^8-b^10+a^8 c^2-4 a^6 b^2 c^2+2 a^4 b^4 c^2-a^2 b^6 c^2+2 b^8 c^2-2 a^6 c^4+2 a^4 b^2 c^4-b^6 c^4-a^2 b^2 c^6-b^4 c^6+2 a^2 c^8+2 b^2 c^8-c^10) : : = X(11649) in ETC now (2017-01-10).

K888 is an isogonal pK with pivot S in a (yellow) triangle GPQ where P, Q are rather complicated and not detailed here. These points are Psi-inverses.

The singular focus F is complicated with SEARCH = 2.32132544307097.