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

too complicated to be written here. Click on the link to download a text file.

X(2), X(3), X(55), X(574), X(47047), X(47048), X(47049), X(47050), X(47051)

midpoints of ABC

extraversions of X(55)

infinite points of K243 = pK(X6, X376)

vertices of the Thomson triangle Q1Q2Q3

vertices of the CircumTangential triangle T1T2T3

Geometric properties :

X1265 is the Thomson-isogonal transform of the nodal stelloid K1264.

K1265 is a nodal cubic with node O and the nodal tangents are parallel to the asymptotes of the Jerabek hyperbola.

The asymptotes are parallel to those of the cubic K243. The two cubics meet again at six finite points that lie on the rectangular hyperbola (H) passing through X3, X6, X20, X193, X2293, X2574, X2575, X3057, etc. (H) is the polar conic of O in K1265.

See Table 25 and Table 56.

The anticomplement of K1265 is K1301.

A construction :

Let M be a point on the circumcircle (O) and M* its isogonal conjugate at infinity. The parallel at M to the line GM* meets (O) again at M'. The lines GM' and OM meet at N on K1265.