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