Length of Angle Bisector/Proof 1

Proof
Similarly, or by symmetry, we get:
 * $BD = \dfrac {a c} {b + c}$

From Stewart's Theorem, we have:
 * $b^2 \cdot BD + c^2 \cdot DC = d^2 \cdot a + BD \cdot DC \cdot a$

Substituting the above expressions for $BD$ and $DC$: