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In Delta ABC if tan(A/2) tan(B/2) + tan(...

In `Delta ABC if tan(A/2) tan(B/2) + tan(B/2) tan(C/2) = 2/3 ` then `a+c`

A

3b

B

2b

C

3b/2

D

4b

Text Solution

Verified by Experts

The correct Answer is:
B
`tan.(A)/(2)tan.(B)/(2)+tan.(B)/(2)tan.(C )/(2)=(2)/(3)`
`rArr sqrt(((s-b)(s-c))/(s(s-a)))sqrt(((s-a)(s-c))/(s(s-b)))+sqrt(((s-a)(s-c))/(s(s-b)))sqrt(((s-a)(s-b))/(s(s-c)))=(2)/(3)`
`rArr (s-c)/(s)+(s-a)/(s)=(2)/(3)`
`rArr 3(2s-a-c)=2s`
`rArr 3b=a+b+c`
`rArr a+c=2b`
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