Question

In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If AB = 10 cm, AC = 14 cm, and BC = 6 cm, find BD and DC.

Answer 1

Given: In Δ ABC, AD is the bisector of ∠A meeting side BC at D. And, AB = 10 cm, AC = 14 cm, and BC = 6 cm 

Required to find: BD and DC.

Since, AD is bisector of ∠A 

We have, \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\) (AD is bisector of ∠A and side BC) 

Then, \(\frac{10}{14}\) = \(\frac{x}{(6 – x)}\)

14x = 60 – 6x 

20x = 60 

x = \(\frac{60}{20}\) 

∴ BD = 3 cm and DC = (6 – 3) = 3 cm.