In the plane of any triangle ABC, let
D = midpoint of BC,
X = center of the A-excircle,
The lines DX, EY, FZ meet in a point, labeled M in the figure. The point was studied by C. von Nagel in 1836, and is called the Mittenpunkt in
Peter Baptist, Die Entwicklung der Neueren Dreiecksgeometrie,Wissenschaftsverlag, Mannheim, 1992, page 72.
The Mittenpunkt is the symmedian point of triangle XYZ.