Length of Angle Bisector in terms of Angle

Theorem
Let $\triangle ABC$ be a triangle with sides $a$, $b$ and $c$ opposite vertices $A$, $B$ and $C$ respectively.

Let $AD$ be the angle bisector of $\angle BAC$ that intersects $a$ at $D$.


 * LengthOfAngleBisector.png

Then:
 * $AD = \dfrac {2 c b \cos \frac A 2} {b + c}$

Proof
Then: