In the plane of any triangle ABC, let

D = midpoint of BC,
E = midpoint of CA,
F = midpoint of AB;

X = center of the A-excircle,
Y = center of the B-excircle,
Z = center of the C-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.

Triangle Centers
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