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K198 is an isotomic equilateral nK. Its root is X(76), the isotomic conjugate of K. It is a member of the class CL005 of cubics.

The triangle formed by the asymptotes is centered at X(381) midpoint of GH and its inradius is R.

K198 contains the following points :

  • the points at infinity of the sidelines of the (first) Morley triangle.
  • their isotomic conjugates Ta, Tb, Tc. These are the common points (together with X(99), the Steiner point) of the Steiner ellipse (S) and the circle (C) centered at X(76) passing through X(99). TaTbTc is equilateral. See " A Morley Configuration" in the Downloads page.
  • the intersections U, V, W of the de Longchamps axis and the sidelines
  • A', B', C' common tangentials of A, B, C and U, V, W respectively, on the trilinear polar (D) of the isogonal conjugate of X(1506). The tangents at A, B, C are the sidelines of the tangential triangle.


Floor van Lamoen has found a geometric characterization of K198 he describes in Hyacinthos, message #10825.

The isogonal transform of K198 is K409.