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

X(1), X(2), X(6), X(141), X(251), X(2896), X(2916), X(3961), X(7194)


A', B', C' : cevians of X(141) in ABC

common points of the Steiner ellipse (S) and pK(X2, X384)

cevians of X(251) in A'B'C' hence K655 is a pK with pivot X(251) in A'B'C'


The radical axes of the circumcircle (O) and the second Neuberg circles N2a, N2b, N2c bound a triangle TaTbTc homothetic to ABC at X(251) and to the medial triangle at the barycentric product X(141) x X(7829) with SEARCH = 3.21492390998425.

TaTbTc is perspective to the cevian triangle of every point on the cubic K655.

TaTbTc is orthologic to the cevian triangle of every point on K007.


The isotomic transform of K655 is pK(X76, X8024).

The symbolic substitution SS{a -> √a} transforms K655 into K328.

K655 is a member of the Thomson-Grebe pencil. See Table 13.