SAT1000 - P370

Geometry Level pending

Given that in $\triangle ABC$ , $\sin 2A+\sin(A-B+C)=\sin(C-A-B)+\dfrac{1}{2}$ , $S$ is the area of $\triangle ABC$ , $1 \leq S \leq 2$ , let $a,b,c$ be the opposite side of angle $A,B,C$ respectively.

Which inequality always holds?

$A.\ bc(b+c)>8$

$B.\ ab(a+b)>16 \sqrt{2}$

$C.\ 6 \leq abc \leq 12$

$D.\ 12 \leq abc \leq 24$

Have a look at my problem set: SAT 1000 problems