Question

In a ∆ABC, it is given that AD is the internal bisector of ∠A. If AB = 10 cm, AC = 14 cm and BC = 6 cm, then CD = ?


(a) 4.8 cm
(b) 3.5 cm
(c) 7 cm
(d) 10.5 cm

Answer 1

(b) 3.5 cm

It is given that AD bisects angle A.
Therefore, applying angle bisector theorem, we get:

$$\begin{gathered} \frac{BD}{DC}=\frac{10}{14} \\ \Rightarrow \frac{6-X}{X}=\frac{10}{14} \\ \Rightarrow 14\times \left(6-X\right)=10X \\ \Rightarrow 84-14X=10X \\ \Rightarrow 84=10X+14X \\ \Rightarrow 84=24X \\ \Rightarrow 24X=84 \\ \Rightarrow X=\frac{84}{24}=3.5 \end{gathered}$$

Hence, CD = 3.5 cm