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In a triangle ABC, (a+b+c)(b+c-a)=kbc if...

In a triangle ABC, (a+b+c)(b+c-a)=kbc if

A

`k lt 0`

B

`k gt 0`

C

`0 lt k lt 4`

D

`k lt 4`

Text Solution

Verified by Experts

The correct Answer is:
C
`(a + b + c) (b + c -a) = kbc`
or `(b + c)^(2) -a^(2) = kbc`
or `b^(2) + c^(2) -a^(2) = (k -2) bc`
or `2bc cos A = (k -1) bc`
or `cos A = (k -2)/(2)`
Now, A being the angle of a triangle, we have
`-1 lt cos A lt 1 " or " -2 lt k - 2 lt 2 " or " 0 lt k lt 4`
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