Home page | Catalogue | Classes | Tables | Glossary | Notations | Links | Bibliography | Thanks | Downloads | Related Curves

see below

K196 = nK0(X76, X2) is the isotomic transform of the Kjp cubic K024.

It is in fact a nK0+ with three asymptotes parallel at X(76) to the sidelines of ABC. The circle (C) centered at X(76) passing through X(99) = Steiner point is tritangent to K196 at Ta, Tb, Tc vertices of an equilateral triangle. See "A Morley Configuration" in the Downloads page.

K196 intersects its asymptotes at Sa, Sb, Sc lying on the trilinear polar (L) of the X(76)-isoconjugate of X(39). This point has barycentric coordinates : 1 / [a^4(b^2+c^2)] : : . The tangents at A, B, C pass through Sa, Sb, Sc respectively and form a triangle whose vertices are the harmonic associates of X(76). The circum-conic with perspector X(76) is inscribed in this triangle and is tritangent at A, B, C to K196.

The pencil F of conics through Ta, Tb, Tc, X(99) already contains the Steiner ellipse and (C) : all the conics have the same directions of axes. Thus, F contains a rectangular hyperbola through Ta, Tb, Tc, X(99), X(76) having the same asymptotic directions as the circum rectangular hyperbola through X(99) : this hyperbola has center X(114) and is the isogonal transform of the perpendicular at O to the Brocard axis. Obviously, F contains also two parabolas.