proof of bisectors theorem

Notice that the trianglesMathworldPlanetmath BAP and CAP have the same common height h, and if (BAP) and (CAP) denote their respective areas, we have


On the other hand


and so


We have obtained


which is the generalizationPlanetmathPlanetmath to the theorem. In the particular case when AP is the bisectorMathworldPlanetmath, BAP=CAP, and thus sinBAP=sinCAP. Cancelling out the sines proves the bisector theorem.

Title proof of bisectors theoremPlanetmathPlanetmath
Canonical name ProofOfBisectorsTheorem
Date of creation 2013-03-22 14:49:25
Last modified on 2013-03-22 14:49:25
Owner drini (3)
Last modified by drini (3)
Numerical id 6
Author drini (3)
Entry type Proof
Classification msc 51A05