bisectors theorem

Bisectors theorem.
Let ABC a triangle, and AP the angle bisectorMathworldPlanetmath of CAB. Then


Generalization of bisectors theorem.
Let ABC a triangle, and P any point on the side BC. Then


The latest theorem even holds when P is not on the segment BC but anywhere on the line (possibly at the infnity), but in this case, the ratio BP/PC must be done with directed segments and the angles considered as directed angles.

Title bisectors theorem
Canonical name BisectorsTheorem
Date of creation 2013-03-22 14:49:23
Last modified on 2013-03-22 14:49:23
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Theorem
Classification msc 51A05
Synonym angle bisector theorem
Synonym generalization of bisectors theorem
Related topic CevasTheorem
Related topic HarmonicDivision