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

X(3), X(4), X(5), X(52), X(68), X(155), E(593) feet of altitudes and their reflections in X(5) (these points on the perpendicular bisectors) reflections of A, B, C in X(5) : centers of circles HBC, HCA, HAB i.e. centers of the Johnson circles 

The Euler cubic is the central pK with center X(5), pivot X(4), pole X(216). It is the Darboux cubic of the orthic triangle. See the related K627. It is the locus of point M such that the parallels at M to AO, BO, CO meet the corresponding sidelines of ABC in three points forming a triangle perspective to ABC. The locus of the perspector is a remarkable isotomic pK with pivot X(264) called Euler perspector cubic. See other locus properties in the page K646 and here (Angel Montesdeoca) and also K612 and K674 (César Lozada). 
