Length of Angle Bisector

Theorem
Let $\triangle ABC$ be a triangle.

Let $AD$ be the angle bisector of $\angle BAC$ in $\triangle ABC$.


 * LengthOfAngleBisector.png

Let $d$ be the length of $AD$.

Then $d$ is given by:


 * $d^2 = \dfrac {b c} {\paren {b + c}^2} \paren {\paren {b + c}^2 - a^2}$

where $a$, $b$, and $c$ are the sides opposite $A$, $B$ and $C$ respectively.