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, the CD = ?
(a) 4.8 cm
(b) 3.5 cm
(c) 7 cm
(d) 10.5 cm

Answer 1

By using angle bisector theore in △ABC, we have
$$\begin{gathered} \frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{BD}}{\mathrm{DC}} \\ \Rightarrow \frac{10}{14}=\frac{6-x}{x} \\ \Rightarrow 10x=84-14x \\ \Rightarrow 24x=84 \\ \Rightarrow x=3.5 \end{gathered}$$
Hence, the correct answer is option (b).