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K919

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X(3), X(4), X(24), X(54), X(96), X(254), X(6193), X(8883), X(8884), X(14517), X(14518)

vertices of the cevian triangle of X(8884)

vertices of the circumcevian triangle of X(4)

infinite points of K364

points of pK(X6, X5889) on (O)

isogonal conjugates of the vertices of the Johnson triangle, of the reflection in X(5) of the vertices of the orthic triangle

Geometric properties :

K919 is pK(X8882, X8884), the isogonal transform of K044.

X(4) is a point of inflexion with tangent passing through X(6).

The isopivot of K919 is X(3) hence the tangents at A, B, C, X(8884) concur at X(3).

Locus properties :

  1. K919 is the locus of P such that the cubic denoted (K) in Table 43 is a psK.
  2. The locus of M whose anticevian triangle is perspective to the circumcevian triangle of X(4) is the cubic pK(X8882, X275) passing through X(2), X(4), X(6), X(54), X(275), X(1993), X(8882). The locus of the perspector is K919. See CL043 for a generalization.