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In DeltaABC,(a+b-c)(b+c-a)(c+a-b)-abc is...

In `DeltaABC,(a+b-c)(b+c-a)(c+a-b)-abc` is always

A

non -negative

B

non -positive

C

negative

D

positive

Text Solution

Verified by Experts

The correct Answer is:
B
`(a+b-c)(b+c-a)(c+a-b)-abc`
`=8(s-c)(s-a)(s-b)-abc`
`=8*(Delta^(2))/(s)-R*4Delta=4Delta((2Delta)/(s)-R)`
`=4Delta(2r-R)le0`
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