Question

In a $△ABC,$ if 2s = a + b + c and (s-b)(s-c)=x $si{n}^2\frac{A}{2},$ then x = [MP PET 1992]

• A. bc
• B. ca
• C. ab
• D. abc

Answer 1

The correct option is A

bc

$sin\frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{bc}}\Rightarrow bcsi{n}^2\frac{A}{2}=(s-b)(s-c)$
Hence x = bc.