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K790

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X(2), X(4), X(6), X(194), X(262), X(3168), X(6776), X(7735), X(9307), X(9755)

vertices of the cevian triangle of X(6)

isopivot : 3a^2 + (b^2 - c^2)^2 / a^2 : : , on many lines such as X(2)X(39), X(4)X(51), X(6)X(264), etc

K790 is the locus of M such that the anticevian triangle of M and the Artzt triangle are perspective. The locus of the perspector is pK(X7735, X9756). (César Lozada, see the preamble of X(9742) in ETC). See the related K677 where "anticevian" is replaced with "cevian".

K677 and K790 generate a pencil of circum-cubics which also contains K791 = pK(X263, X262) – the third and last pK of the pencil – and the union of the Euler line with the Kiepert hyperbola. All these cubics contain A, B, C, X(2), X(4), X(6), X(262) and two imaginary points P1, P2. These points are X(7735)-isoconjugate, symmetric about X(6) and they lie on the perpendicular at X(6) to the Euler line.

Remark : one of the cubics of the pencil passes through the vertices of the Artzt triangle.