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

points at infinity of the Morley sidelines

their isotomic conjugates Ta, Tb, Tc

All isotomic nK60 cubics form a pencil of cubics with roots on the line X(2)X(76). See Special Isocubics §7.3. They form the class CL005 of cubics.

This pencil contains only one nK60+ which is K094 and four cK60, the one with singularity G being K089. See also K198.

They all pass through A, B, C, the infinite points of the Morley triangle sidelines and their isotomic conjugates Ta, Tb, Tc on the Steiner circum-ellipse and on the circle centred at X(76) passing through X(99)..

The centers of the equilateral triangles formed with the asymptotes lie on the parallel at X(381) to the Brocard axis OK.

The pencil contains one and only one nK0 which is K093. Its root is X(7757), the reflection of X(76) in G, the midpoint of G, X(194).