In $\triangle ABC$, $AB = 5$, $AC = 10$, $BC = 12$. If $AD$ bisects $\angle A$, $BD = ?$

By the Internal Bisector Theorem, $BD:DC = AB:AC = 5:10 = 1:2$. Therefore $BD = \dfrac{1}{1+2} \times BC = \dfrac{1}{3} \times 12 = 4$.