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K661

a (b - c) x (c^2y^2 - b^2z^2) = 0

X(1), X(100), X(513), X(1054)

isogonal X(1054)* of X(1054)

excenters

traces of X(513)

K661 is the locus of P such that the sum of the algebraic distances from P to the sidelines of ABC (sometimes called absolute normal coordinates) is equal to that of its isogonal conjugate P* (Lemoine, AFAS Pau 1892, p.121). See the related cubic K662.

K661 is a circular cubic with focus X(104), the reflection of X(100) about O.

See Table 12 for other circular cubics with pivot P ≠ H.

If P* is replaced with the image of P under the isoconjugation with pole Ω, then the the locus of P becomes pK(Ω, X513).