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X(2), X(3), X(6), X(69), X(485), X(486), X(8770)

X(2)-Ceva conjugate of X(69)

midpoints

CPCC or H-cevian points, see Table 11

foci of the K-ellipse (inellipse with center K when the triangle ABC is acute angle)

K168 is the pivotal cubic whose GST (see here for a definition) is the de Longchamps line. See K167. See also K007, property 8 and K002, property 12.

It is also the locus of point P such that P, GSC(P), X(6) are collinear. GSC is defined here.

It has the same asymptotic directions as pK(X6, X193) and K170 = pK(X2, X4) which is actually its anticomplement.

It meets the circumcircle at the same points as pK(X6, X69) = K169 and the Steiner circum-ellipse at the same points as pK(X2, X76) = K141. It is tangent at O to the Brocard line, at G to the Euler line.

Its isogonal transform is pK(X25, X4) = K233 and its isotomic transform is pK(X264, X264). See CL007.

K168 is an isogonal pK with pivot X(6) with respect to the complement of the orthic triangle.