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.
