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In a triangle ABC if tan.(A)/(2)tan.(B)/...

In a triangle ABC if `tan.(A)/(2)tan.(B)/(2)=(1)/(3)` and ab = 4, then the value of c can be

A

1

B

`1.5`

C

`2.5`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`tan.(A)/(2).tan.(B)/(2)=(1)/(3)`
`rArr sqrt(((s-b)(s-c))/(s(s-a)))sqrt(((s-a)(s-c))/(s(s-b)))=(1)/(3)`
`rArr (s-c)/(s)=(1)/(3)`
`rArr 2s=3c`
`rArr a+b=2c`
Now `(a+b)/(2)ge sqrt(ab)`
`rArr c ge 2`
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