# ABC is a triangle whose sides AB = 6 cm, BC = 8 cm and AC = 12 cms. D is such a point situated on AC that angle ADB = angle ABC. Find the length of BD ?

Jan 7, 2017

In $\Delta A B D \mathmr{and} \Delta A B C$

• $\angle B A D = \angle B A C \left(\text{common}\right)$
• $\angle A D B = \angle A B C \left(\text{given}\right)$

• $\angle A B D = \angle A C B \left(\text{remaining}\right)$

So $\Delta A B D \mathmr{and} \Delta A B C$ are SIMILAR

Hence

$\frac{B D}{B C} = \frac{A B}{A C}$

$B D = \frac{A B \times B C}{A C} = \frac{6 \times 8}{12} = 4 c m$