The (interior) bisector of an angle , also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line
or line segment that divides the angle into two equal
parts.
The angle bisectors meet at the incenter , which has trilinear
coordinates 1:1:1.
The length
of the bisector
of angle in the above triangle is given by
where
and .
The points ,
, and have trilinear coordinates , , and , respectively, and form the vertices of the incentral
triangle .
See also Angle ,
Angle Bisector Theorem ,
Angle Trisection ,
Cyclic
Quadrangle ,
Exterior Angle Bisector ,
Incenter ,
Incentral
Triangle ,
Incircle ,
Isodynamic
Points ,
Orthocentric System ,
Steiner-Lehmus
Theorem
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References Altshiller-Court, N. College Geometry: A Second Course in Plane Geometry for Colleges and Normal Schools, 2nd
ed., rev. enl. New York: Barnes and Noble, p. 18, 1952. Coxeter,
H. S. M. and Greitzer, S. L. Geometry
Revisited. Washington, DC: Math. Assoc. Amer., pp. 9-10, 1967. Dixon,
R. Mathographics.
New York: Dover, p. 19, 1991. Kimberling, C. "Triangle Centers
and Central Triangles." Congr. Numer. 129 , 1-295, 1998. Mackay,
J. S. "Properties Concerned with the Angular Bisectors of a Triangle."
Proc. Edinburgh Math. Soc. 13 , 37-102, 1895. Pedoe, D.
Circles:
A Mathematical View, rev. ed. Washington, DC: Math. Assoc. Amer., pp. xiv-xv,
1995. Referenced on Wolfram|Alpha Angle Bisector
Cite this as:
Weisstein, Eric W. "Angle Bisector." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/AngleBisector.html
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