# Triangle center

In the geometry is meant by the excellent points (also: strange points ) of a triangle in the first place the following four points:

- The orthocenter H (intersection of heights),
- The circumcenter U ( intersection of the perpendicular bisectors ( Seitensymmetralen ) )
- The incenter I ( the intersection of the angle bisector ( Winkelsymmetralen )), and
- The center of gravity S ( intersection of the medians (heavy lines)).

The orthocenter, the circumcenter and the centroid always lie on a straight line, the Euler's line. On it, in the middle between H and U, is also the center of Feuerbach circle.

## More points after the Encyclopedia of Triangle Centers

In addition to the four "classic" excellent points of a triangle (focus, circumcenter, incenter, orthocenter ), which were already known in antiquity, were found and studied many other points in the last centuries. Clark Kimberling 's Encyclopedia of Triangle Centers ( see web link) leads to more than 5400 special points and their main characteristics. Introduced in this directory default name consisting of the letters X and an index that is used today in many treatises on the triangle geometry. The following table lists some important examples:

## Related Topics

In addition to individual points can be a triangle also assign different tuple of points:

- Morley triangle
- Napoleon Triangle
- Höhenfußpunktdreieck
- Brocard points
- Johnson Triangle
- Kiepert Triangle

Special circuits are:

- Circumference, inscribed circle, excircles
- Feuerbach circle ( nine-point circle)
- Lamoen Circle
- Taylor Circle
- Johnson Circles