A) \[\tan \frac{\pi }{8}\]
B) \[2\tan \frac{\pi }{8}\]
C) \[\cot \frac{\pi }{8}\]
D) \[\frac{1}{2}\cot \frac{\pi }{8}\]
Correct Answer: C
Solution :
\[{{A}_{0}}r_{0}^{2}=\pi ;\] Let \[r={{r}_{0}}+1\]then\[A=2{{A}_{0}}\] \[\therefore \] \[\pi {{({{r}_{0}}+1)}^{2}}=2\pi \] \[\Rightarrow \] \[r_{0}^{2}-2{{r}_{0}}-1=0\] \[\Rightarrow \] \[{{r}_{0}}=\frac{2\pm \sqrt{4+4}}{2}=1+\sqrt{2}=\cot \frac{\pi }{8}\]
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