C.a.R. >
Applications >
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 green triangle.
- 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 triangle.