Question

In a ΔABC, 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

In ΔABC, AD is the bisector of ∠A.

We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

`therefore"BD"/"DC"="AB"/"AC"`

`rArrx/(12-x)=10/6`

⇒ 6x = 10(12 – x)

⇒ 6x = 120 – 10x

⇒ 6x + 10x = 120

⇒ 16x = 120

`rArrx=120/16=7.5 ` cm

∴ BD = 7.5 cm and DC = 12 – x = 12 – 7.5 = 4.5 cm

Hence, BD = 7.5 cm and DC = 4.5 cm