Triangle Geometry > Euler line
- In the green triangle, U is the orthocenter, as we saw
in the beginning. In the black one, U is the center
of the circumcircle.
- Moreover, U* is the center of the circumcircle of the
- S is on AA*, BB* and CC*. Consequently, it is the
barycenter of the black triangle. Since the green triangle is the dilatation
of the black one, S is also the barycenter of the green triangle.
Thus, S is between U and U* and SU=2SU*.
The green circle is the
nine point circle of the black