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X(2), X(6), X(5969), X(5970), X(39641), X(39642)

Ω1, Ω2 Brocard points

X(39641), X(39642) are the imaginary foci of the Brocard inellipse, on the Brocard axis and the Kiepert hyperbola

K688 is a member of the class CL061.

It is a focal cubic with singular focus F on the circumcircle, the locus of M such that (MG, MΩ1)+(MK, MΩ2) = 0 (mod. π) or the locus of foci of inconics with center on the line through X(39), X(597).

F lies on the lines X(6)X(805), X(32)X(691), X(99)X(187), X(110)X(1691), X(111)X(669), etc. SEARCH = 1.47609410848068.

The isogonal conjugate F* is the real point at infinity, on the lines X(2)X(694), X(6)X(99), X(39)X(597), X(69)X(148), X(76)X(338), X(98)X(1350), X(115)X(141), etc. SEARCH = 2.75454271260382.

F and F* are now X(5970), X(5969) in ETC.