# In a ∆ABC, AD is the bisector of ∠BAC. If AB = 6 cm, AC = 5 cm and BD = 3 cm, then DC =

Question:

In a ∆ABC, AD is the bisector of ∠BAC. If AB = 6 cm, AC = 5 cm and BD = 3 cm, then DC =

(a) 11.3 cm
(b) 2.5 cm
(c) 3 : 5 cm
(d) None of these

Solution:

Given: In a $\triangle \mathrm{ABC}, \mathrm{AD}$ is the bisector of $\angle \mathrm{BAC} . \mathrm{AB}=6 \mathrm{~cm}$ and $\mathrm{AC}=5 \mathrm{~cm}$ and $\mathrm{BD}=3 \mathrm{~cm}$.

To find: DC

We know that the internal bisector of angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

Hence,

$\frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{BD}}{\mathrm{DC}}$

$\frac{6}{5}=\frac{3}{\mathrm{DC}}$

$\mathrm{DC}=\frac{5 \times 3}{6}$

$\mathrm{DC}=2.5 \mathrm{~cm}$

Hence we got the result $(b)$