A) \[\sqrt{3}\]
B) \[\sqrt{2}\]
C) \[b\sin A=a,A<\frac{\pi }{2}\]
D) 0
Correct Answer: D
Solution :
Area\[=\frac{1}{2}\left| \begin{matrix} a & b+c & 1 \\ b & c+a & 1 \\ c & c+b & 1 \\ \end{matrix} \right|\] \[=\frac{1}{2}\left| \begin{matrix} a & a+b+c & 1 \\ b & a+b+c & 1 \\ c & a+b+c & 1 \\ \end{matrix} \right|\] applying \[{{C}_{2}}\to {{C}_{1}}+{{C}_{2}}\] \[=\frac{(a+b+c)}{2}\left| \begin{matrix} a & 1 & 1 \\ b & 1 & 1 \\ c & 1 & 1 \\ \end{matrix} \right|=0\]
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