In a ΔABC, AD is the bisector of ∠A.

If AB = 10 cm, AC = 14 cm and BC =6 cm, find BD and DC.

Given: AB = 10 cm, AC = 14 cm and BC = 6 cm

Since AD bisects ∠A, we can apply angle-bisector theorem in ∆ABC,

Substituting given values, we get

To find BD and DC,

Let BD = x cm, and it’s given that BC = 6 cm, then DC = (6 – x) cm

Then

⇒ 14x = 10(6 – x)

⇒ 14x = 60 – 10x

⇒ 14x + 10x = 60

⇒ 24x = 60

⇒ x = 60/24 = 2.5

⇒ BD = 2.5 cm

If BD = 2.5 cm and BC = 6 cm, then DC = (6 – x) = (6 – 2.5) = 3.5

Thus, BD is 2.5 cm and DC = 3.5 cm.