Question

In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC =  5 cm, then CD =

Options

•  2 cm

•  3 cm

•  4 cm

•  5 cm

Answer 1

It is given that

 AC, is bisector of ∠BAD

∠BAC = ∠CAD

AB =  3cm

AC =5cm

We are to find the side CD

Analyze the figure and conclude that

 CD = BC (As in the two triangles are congruent)

In ΔABC

`BC = sqrt25- 9`

    `= sqrt 16`

      = 4

So 

BC = CD

⇒ CD = 4

Hence (c)  CD = 4.