The mittenpunkt (also called the middlespoint) of a triangle 
is the symmedian
point of the excentral triangle, i.e.,
the point of concurrence 
of the lines
from the excenters 
through the corresponding triangle side midpoints 
.
It is commonly denoted 
or 
, has equivalent triangle
center functions
 |  |  |
(1)
|
 |  |  |
(2)
|
and is Kimberling center 
(Kimberling 1998, p. 66).
|
|
The mittenpunkt is collinear with the Gergonne point 
and triangle centroid 
, with 
. The mittenpunkt is
also collinear with the Spieker
center 
and the orthocenter (Eddy 1990). Further, the mittenpunkt
is collinear with the incenter 
and symmedian
point 
of 
, with distance ratio
 |
(3)
|
Distances from the mittenpunkt to several other named triangle centers include
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
where 
is the Clawson point, 
is the orthocenter, 
is the incenter, 
is the symmedian point,
and 
is the Spieker
center.
The mittenpunkt is the center of the Mandart inellipse and the billiard circumellipse (Reznik and Garcia 2021, p. 33).
