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 I, which has trilinear coordinates 1:1:1.


The length t_1 of the bisector A_1T_1 of angle A_1 in the above triangle DeltaA_1A_2A_3 is given by


where t_i=A_iT_i^_ and a_i=A_jA_k^_.

The points T_1, T_2, and T_3 have trilinear coordinates (0,1,1), (1,0,1), and (1,1,0), 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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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.

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Angle Bisector

Cite this as:

Weisstein, Eric W. "Angle Bisector." From MathWorld--A Wolfram Web Resource.

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