$∆ABC$是边长为2的等边三角形，已知向量$\stackrel{\rightharpoonup }{a},\stackrel{\rightharpoonup }{b}$满足$\stackrel{\rightharpoonup }{AB}=2\stackrel{\rightharpoonup }{a},\stackrel{\rightharpoonup }{AC}=2\stackrel{\rightharpoonup }{a}+\stackrel{\rightharpoonup }{b}$，则下列结论正确的是（）

A．

$\left|\stackrel{\rightharpoonup }{b}\right|=1$

B．

$\stackrel{\rightharpoonup }{a}\perp \stackrel{\rightharpoonup }{b}$

C．

$\stackrel{\rightharpoonup }{a}·\stackrel{\rightharpoonup }{b}=1$

D．

$\left(4\stackrel{\rightharpoonup }{a}+\stackrel{\rightharpoonup }{b}\right)\perp \stackrel{\rightharpoonup }{BC}$