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Question

In Fig. 4.60, check whether AD is the bisector of ∠A of ∆ABC in each of the following:

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm
(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm
(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

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Solution

(i) It is given that,, and .

We have to check whether is bisector of .

First we will check proportional ratio between sides.

Now

ABAC=510=12

BDCD=1.53.5=37

Since ABACBDCD

Hence is not the bisector of .

(ii) It is given that,,, and .

We have to check whether is bisector of .

First we will check proportional ratio between sides.

So
46=1.62.423=23

(It is proportional)

Hence, is bisector of .

(iii) It is given that,,, and .

We have to check whether is bisector of .

First we will check proportional ratio between sides.

Now



So


(It is proportional)

Hence, is bisector of .

(iv) It is given that, AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm.

We have to check whether is bisector of .

First we will check proportional ratio between sides.

So

68=1.5234=34

(It is proportional)

Hence is bisector of .

(v) It is given that AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

We have to check whether is bisector of .

First we will check proportional ratio between sides.

Now

ABAC=512

BDCD=2.59=518

Since ABACBDCD

Hence is not the bisector of .


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