The radius of a circle, having minimum area, which touches the curve $y=4-x^2$and the lines $y=\left|x\right|$is :$4\left(\sqrt{2}-1\right)$ (2) $4\left(\sqrt{2}+1\right)$ (3) $2\left(\sqrt{2}+1\right)$ (4) $2\left(\sqrt{2}-1\right)$

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