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# Angle Bisector

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.

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.

Angle Bisector

## Cite this as:

Weisstein, Eric W. "Angle Bisector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AngleBisector.html