A) \[{{x}^{2}}+{{y}^{2}}=3-\sqrt{2}\]
B) \[{{x}^{2}}+{{y}^{2}}=6-3\sqrt{2}\]
C) \[{{x}^{2}}+{{y}^{2}}=5-2\sqrt{2}\]
D) \[{{x}^{2}}+{{y}^{2}}=3-2\sqrt{2}\]
Correct Answer: D
Solution :
\[{{A}_{1}}{{B}_{1}}=\sqrt{4+4}=2\sqrt{2}\] \[AB=2\sqrt{2}-2=2(\sqrt{2}-1)\] \[\Rightarrow \]\[OA=AB=\frac{AB}{2}=\sqrt{2}-1\]which is the radius of required circle. Thus, equation of required circle is \[{{x}^{2}}+{{y}^{2}}={{(\sqrt{2}-1)}^{2}}=3-2\sqrt{2}\]You need to login to perform this action.
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