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K081 is a member of the class CL020 of "equal power cubics".

It is the locus of point P whose pedal circle passes through H i.e. is orthogonal to the circle centered at H with radius 0. Hence, K081 is a member of the class CL036.

The power of any point P on the cubic with respect to its pedal circle is constant. Its value is -4R^2 cosA cosB cosC.

K081 is an isogonal nK with root X(2) = G. Its asymptotes are parallel to the sidelines of ABC and meet the cubic again at three points on a perpendicular to the Brocard line.