In $\triangle ABC$, $AB = 8$, $AC = 6$, $BC = 14$. If $AD$ bisects $\angle A$, $BD = ?$

By the Internal Bisector Theorem, $BD:DC = AB:AC = 8:6 = 4:3$. Hence $BD = \dfrac{4}{4+3} \times BC = \dfrac{4}{7} \times 14 = 8$.