The radius of a circle, having minimum area, which touches the curve $y=4−x^2$ and the lines, $y=|x|$ is :

Question

$\begin{array}{1 1} (1) 2(\sqrt{2}-1) \\ (2)4(\sqrt{2}-1) \\ (3) 4(\sqrt{2}+1) \\ (4) 2(\sqrt{2}+1)\end{array} $