Nagel point

The nail - point, named after the German mathematician Christian Heinrich von Nagel (1803-1882), one of the special points of a triangle. For a given triangle ABC are regarded as the points D, E and F, in which the excircles contact the sides of the triangle. By connecting those points of contact with the opposite corners of the triangle (ie A, B or C), then these links intersect at a point N. This is referred to as nail - point of the triangle.

Coordinates

Properties

• Looking out the nail - point N of the triangle ABC and the incenter I and the center of gravity S, then the points N, S and I on a straight line, the nail straight, and it is considered, focusing S between points N and I is. In this capacity, the nail straight has an analogy to the Euler's line.
• The Spieker - point is the midpoint of the line segment connecting nail point and incenter and thus also lies on the nail straight.
• The nail point and the point Gergonne - conjugated isotomisch.