A) \[abc\]
B) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]
C) \[ab+bc+ca\]
D) 0
Correct Answer: D
Solution :
Area of triangle \[=\frac{1}{2}\left| \,\begin{matrix} a & b+c & 1 \\ b & c+a & 1 \\ c & a+b & 1 \\ \end{matrix}\, \right|\] \[=\frac{1}{2}\left| \,\begin{matrix} a+b+c & b+c & 1 \\ b+c+a & c+a & 1 \\ c+a+b & a+b & 1 \\ \end{matrix}\, \right|\] \[=\frac{1}{2}(a+b+c)\,\left| \begin{matrix} 1 & b+c & 1 \\ 1 & c+a & 1 \\ 1 & a+b & 1 \\ \end{matrix} \right|=0\].
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