Question

In Triangle ABC
(a+b-c)(b+c-a)(c+a-b) -abc is always

• A. Non-Negative
• B. Non-Positive
• C. Negative
• D. Positive

Answer 1

The correct option is A

Non-Negative

(a+b-c)(b+c-a)-abc=8(s-c)(s-b)(s-a)-abc
$=8\frac{{△}^2}{s}-R.4△=4△(\frac{2△}{s}-R)=4△(2r-R)\le 0$