In the plane of any triangle ABC, let
Ea = the Aexcircle, Let
D = the point where Ea touches side BC, The lines AD, BE, CF meet in a point, labeled X in the figure. It is called the Nagel point of triangle ABC.

d = the point half way around the perimeter of ABC, starting at A,
e = the point half way around the perimeter of ABC, starting at B,
f = the point half way around the perimeter of ABC, starting at C,
The lines Ad, Be, Cf meet in the Nagel point.