Question

In a ∆ABC, it is given that AB = 6 cm, AC = 8 cm and AD is the bisector of ∠A. Then, BD : DC =?


(a) 3 : 4
(b) 9 : 16
(c) 4 : 3
(d) $\sqrt{3}:2$

Answer 1

(a) 3 : 4

In ∆ ABD and ∆ACD, we have:
$\angle BAD=\angle CAD$

Now,

$$\begin{gathered} \frac{BD}{DC}=\frac{AB}{AC}=\frac{6}{8}=\frac{3}{4} \\ BD\hspace{0.17em}:DC=3:4 \end{gathered}$$