Question

the angle bisectors BD and CE of a triangle ABC are divided by the incentre I in the ratio 3:2 and 2:1 respectively .Then the ratio. in which I divide the angle bisector through A is​

Answer 1

MATHS

The angle bisectors BD and CE of a triangle ABC are divided by the incentre I in the ratios 3:2 and 2:1 respectively. Then what is the ratio in which I divides the angle bisector through A ?

A

3:1

Your Answer

B

11:4

Correct Answer

C

6:5

D

7:4

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VIDEO EXPLANATION

ANSWER

Incentre divides the angle bisector in a defined ratio of the length of sides of the triangle

IF

AI

=

a

b+c

......(i)

ID

BI

=

b

a+c

=

2

3

⇒2a+2c=3b......(ii)

IB

CI

=

c

a+b

=

1

2

⇒2c=a+b.....(iii)

using (iii) in (ii)

2a+a+b=3b

3a=2b

b=

2

3a

....(iv)

Again 2c=a+b

2c=a+

2

3a

c=

4

5a

.....(v)

using (iv) and (v) in (i)

IF

AI

=

a

2

3a

+

4

5a

=

8

22

=

4

11