Question

In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. If AB = 10 cm, AC = 6 cm, and BC = 12 cm, find BD and DC.

Answer 1

Given: Δ ABC and AD bisects ∠A, meeting side BC at D. AB = 10 cm, AC = 6 cm, and BC = 12 cm. 

Required to find: DC

Since, AD is the bisector of ∠A meeting side BC at D in Δ ABC 

⇒ \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\)

\(\frac{10}{6}\) = BD/ DC …….. (i) 

And, we know that 

BD = BC – DC 

= 12 – DC 

Let BD = x, 

⇒ DC = 12 – x 

Thus (i) becomes, 

\(\frac{10}{6}\) = \(\frac{x}{(12 – x)}\)

5(12 – x) = 3x 

60 - 5x = 3x 

∴ x = \(\frac{60}{8}\) = 7.5 

Hence, DC = 12 – 7.5 = 4.5 cm and BD = 7.5 cm