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

K1118

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

X(3), X(6), X(1995), X(11472), X(33924), X(33925), X(33926), X(33927), X(33928), X(33929)

vertices of these triangles :

• Thomson (points Qi)

• tangential of Thomson (points Ri)

other points below

Geometric properties :

K1118 is a member of the pencil of cubics generated by K172 and K1114. This is studied in Table 71.

K1118 is a nodal cubic with node O, where the tangents are parallel to the asymptotes of the Jerabek hyperbola.

K1118 meets the circumcircle (O) again at T1, T2, T3 on nK0(X6, X7736). These are the antipodes of the common points (apart A, B, C) of (O) and K243 = pK(X6, X376).

K1118 contains the vertices S1, S2, S3 of the tangential triangle of T1T2T3. These points are the common points (apart X2930) of the Stammler hyperbola SH and the circumcircle TC of R1R2R3.

Two perpendicular lines passing through O meet K1118 again at two points collinear with X(1995). It follows that each point M ≠ O on K1118 gives another point N on K1118 : N is the intersection of the line X(1995)M and the perpendicular at O to OM.

 

K1118a