The radius of a circle having minimum area, which touches the curve...

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The radius of a circle having minimum area, which touches the curve \( y=4-x^{2} \) and the lines \( y=|x| \), is
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(a) \( 2(\sqrt{2}+1) \)
(b) \( 2(\sqrt{2}-1) \)
(2017 Main)
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(c) \( 4(\sqrt{2}-1) \)
(d) \( 4(\sqrt{2}+1) \)
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