The point
at which the incircle and nine-point
circle are tangent. It has triangle center
function
(1)
and is Kimberling center .
If
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,
(2)
Distances to some other named triangle centers include
where
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 .
See also Feuerbach Antipode ,
Feuerbach's Theorem ,
Feuerbach Triangle ,
Incircle ,
Nine-Point Circle
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References Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.
Boston, MA: Houghton Mifflin, p. 200, 1929. 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. Washington, DC: Math. Assoc. Amer., 1995. Salmon,
G. Conic
Sections, 6th ed. New York: Chelsea, p. 127, 1960. 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 --A Wolfram Web Resource. https://mathworld.wolfram.com/FeuerbachPoint.html
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