SAT1000 - P370

Geometry Level pending

Given that in ABC\triangle ABC, sin2A+sin(AB+C)=sin(CAB)+12\sin 2A+\sin(A-B+C)=\sin(C-A-B)+\dfrac{1}{2}, SS is the area of ABC\triangle ABC, 1S21 \leq S \leq 2, let a,b,ca,b,c be the opposite side of angle A,B,CA,B,C respectively.

Which inequality always holds?

A. bc(b+c)>8A.\ bc(b+c)>8

B. ab(a+b)>162B.\ ab(a+b)>16 \sqrt{2}

C. 6abc12C.\ 6 \leq abc \leq 12

D. 12abc24D.\ 12 \leq abc \leq 24

Have a look at my problem set: SAT 1000 problems


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