The point incircle and nine-point circle are tangent. It has triangle center function
(1)
and is Kimberling center
If triangle midpoints of the sides
(2)
Distances to some other named triangle centers include
where triangle centroid , incenter , symmedian point , circumcenter , nine-point center , Spieker center , triangle area , and inradius .
See also Feuerbach Antipode ,
Feuerbach's Theorem ,
Feuerbach Triangle ,
Incircle ,
Nine-Point Circle Explore with Wolfram|Alpha References Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67 , 163-187, 1994. Kimberling, C. "Feuerbach Point." http://faculty.evansville.edu/ck6/tcenters/class/feuer.html . Kimberling, C. "Encyclopedia of Triangle Centers: X(11)=Feuerbach Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X11 . PandD Software. "Oppervlakte van voetpuntsdriehoeken, voetpuntscirkels." http://www.pandd.demon.nl/voetpdrieh.htm . Pedoe, D. Circles: A Mathematical View, rev. ed. Salmon, G. Conic Sections, 6th ed. Suceava, B. and Yiu, P. "The Feuerbach Point and Euler Lines." Forum Geom. 6 , 191-197, 2006. http://forumgeom.fau.edu/FG2006volume6/FG200621index.html . Referenced on Wolfram|Alpha Feuerbach Point Cite this as: Weisstein, Eric W. "Feuerbach Point." From MathWorld https://mathworld.wolfram.com/FeuerbachPoint.html
Subject classifications 
at which the incircle and nine-point circle are tangent. It has triangle center function 
. 
is the Feuerbach point a triangle 
and 
, 
, and 
are the midpoints of the sides 
, 
, and 
, respectively, then one of the distances 
, 
, and 
is equal to the sum of the two others. For example, in the above figure, 
is the triangle centroid, 
is the incenter, 
is the symmedian point, 
is the circumcenter, 
is the nine-point center, 
is the Spieker center, 
is the triangle area, and 
is the inradius. 