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Angle bisector theorem

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

Coordinates of the of a triangle

incenter

Circles of Apollonius

This theorem has been used to prove the following theorems/results:

G.W.I.S Amarasinghe: , Global Journal of Advanced Research on Classical and Modern Geometries, Vol 01(01), pp. 15 – 27, 2012

On the Standard Lengths of Angle Bisectors and the Angle Bisector Theorem

at cut-the-knot

A Property of Angle Bisectors

at Khan Academy

Intro to angle bisector theorem