用\(min\{ a{,}b\}\)表示实数\(a{,}b\)中的较小者,已知向量\(\overrightarrow{a}{,}\overrightarrow{b}{,}\overrightarrow{c}\)满足\({|}\overrightarrow{a}{|=}1{,}{|}\overrightarrow{b}{|=}2{,}\overrightarrow{a}{⋅}\overrightarrow{b}{=}0{,}\overrightarrow{c}{=}\lambda\overrightarrow{a}{+}\mu\overrightarrow{b}(\lambda{+}\mu{=}1)\),则当\(min\{\overrightarrow{c}{⋅}\overrightarrow{a}{,}\overrightarrow{c}{⋅}\overrightarrow{b}\}\)取得最大值时,\({|}\overrightarrow{c}{|=}\)