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(3), X(15), X(16), X(23), X(111), X(187), X(5000), X(5001), X(6104), X(6105) inversive images in the circumcircle of X(13), X(14), X(368), foci of the Steiner inellipse, vertices of the fourth Brocard triangle centers of Apollonian circles (inversive images in the circumcircle of the vertices of the second Brocard triangle) 

Let P be a point and Pa, Pb, Pc its inversive images in the Apollonian circles C_a, C_b, C_c respectively. ABC and PaPbPc are perspective if and only if P lies on the circumcircle or on the Apollonius quartic Q049. The inversive image of Q049 in the circumcircle is K018, the second Brocard cubic. Q049 is a bicircular quartic. 
