Question

In a ∆ABC, it is given that AD
is the internal bisector of angle A.
If AB = 10 cm, AC = 14 cm and
BC = 6 cm, then CD = ?
(a) 4.8 cm
(b) 3.5 cm
(c) 7 cm
(d) 10.5 cm​

Answer 1

As we aware of Angle bisector theorem of triangles.

So, using that concept

AB/AC = BD/CD

Let we suppose that CD = x

So, on putting all the values

$\frac{10}{14} = \frac{6 - x}{x}$

$\frac{5}{7} = \frac{6 - x}{x}$

$5x = 42 - 7x$

$12x = 42$

$2x = 7$

$x = 3.5 \: cm$

So, b is correct

CD = 3.5 CM.