In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. Find AC
Question:

In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. Find AC

(a) 4 cm
(b) 6 cm
(c) 3 cm
(d) 8 cm

Solution:

Given: In a ΔABC, AD is the bisector of angle BAC. AB = 8cm, and DC = 3cm and BD = 6cm.

To find: AC

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,

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

$\frac{8}{\mathrm{AC}}=\frac{6}{3}$

$\mathrm{AC}=\frac{8 \times 3}{6}$

$\mathrm{AC}=4 \mathrm{~cm}$

Hence we got the result $(a)$