If a^2 + b^2c^2 = b^2 + c^2a^2 = c^2 + a^2b^2 = 1/k , ( k 0 ) then k = ?

Answer: Option D

$$\begin{array}{rl}& \frac{a^2+b^2}{c^2}=\frac{b^2+c^2}{a^2}=\frac{c^2+a^2}{b^2}=\frac{1}{k}\\ & \text{Put }a=b=c=1\\ & \Rightarrow \frac{1+1}{1}+\frac{1+1}{1}+\frac{1+1}{1}=\frac{1}{k}\\ & \Rightarrow 2=2=2=\frac{1}{k}\\ & \Rightarrow k=\frac{1}{2}\end{array}$$