Question

In a ΔABC, it is given that AD is the internal bisector of ∠A. If AB = 10 cm, AC = 14 cm and BC = 6 cm, then CD = ?

Options

• 4.8 cm

• 3.5 cm

• 7 cm

• 10.5 cm

Answer 1

3.5 cm

Explanation:

By the Angle Bisector Theorem,

`(BD)/(DC) = (AB)/(AC)` 

= `10/14`

= `5/7` 

Let DC = x, so BD = 6 – x.

Then `(6 - x)/x = 5/7`

⇒ 7(6 – x) = 5x

⇒ 42 = 12x

⇒ x = 3.5 cm