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X(2), X(3), X(4), X(69), X(254), X(264), X(1993), X(5392)

isotomic conjugate of X(254)

vertices of antimedial triangle

vertices of the cevian triangle of X(264)

infinite points of pK(X6, X1993)

points of pK(X6, X11442) on the circumcircle

K045 is the isotomic pK with pivot X(264) = isotomic conjugate of X(3).

Locus properties :

  1. locus of perspectors as seen in Euler central cubic.
  2. locus of point P such that the cevian triangle of P and the orthic triangle are orthologic (Hyacinthos #8243-48). See a generalization at Table 7.
  3. locus of point P such that the cevian triangle of P and the tangential triangle are orthologic.
  4. locus of point P such that P, GSC(P), X(1993) are collinear. (X(1993) is the orthocorrespondent of X(3)). GSC is defined here.
  5. Let A'B'C' be the cevian triangle of P. Ab, Ac are the pedals of A' on AC, AB and Ha is the orthocenter of AAbAc. Hb, Hc are defined similarly. Then the locus of P for which ABC and HaHbHc are orthologic is K045 (Paul Yiu, Hyacinthos #9863).
  6. locus of pseudo-pivots of the stelloids psK60+ with asymptotes parallel to those of the McCay cubic K003. See K350.

The isogonal transform of K045 is K176. K045 is also related to Q033.

The complement of K045 is K612 = pK(X216, X2).

See other locus properties in the page K646.