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(1), X(2), X(3), X(15), X(16), X(17), X(18), X(39), X(2896), X(3413), X(3414) midpoints of ABC excenters points of K655 on (O) 

Q140 is a circular quartic passing through the X(5)anticevian points. See Table 28. There are 10 (not always all real) such points. They are represented in black and green on the figure. For example, the ninepoint center of the anticevian triangle of N' is N' itself. O' and H' are the corresponding circumcenter and orthocenter. *** The singular focus of Q104 is X(2080). Q140 has two real asymptotes parallel to those of the Kiepert hyperbola at X = 2a^4+b^4+c^4+4 b^2 c^24 a^2 b^24 a^2 c^2 : : , with SEARCH = 8.11132214901875. X lies on the lines {99,754}, {194,6680}, {230,538}, {325,543}, etc. X is now X(14148) in ETC (20170821). 

The remaining points on the sidelines of ABC are {0 : a^2+2 b^2+c^2 : a^2b^22 c^2}, {2 a^2b^2+c^2 : 0 : a^2+b^22 c^2}, {2 a^2+b^2c^2 : a^22 b^2+c^2 : 0}. 
