已知 $\stackrel{\rightharpoonup }{a},\stackrel{\rightharpoonup }{b}$是平面内两个互相垂直的单位向量，若向量 $\stackrel{\rightharpoonup }{c}$满足 $(\stackrel{\rightharpoonup }{a}-\stackrel{\rightharpoonup }{c})·(\stackrel{\rightharpoonup }{b}-\stackrel{\rightharpoonup }{c})=0$，则 $\left|\stackrel{\rightharpoonup }{c}\right|$的最大值是(   )

A．

1

B．

2

C．

$\sqrt{2}$

D．

$\frac{\sqrt{2}}{2}$