如图，在四边形ABCD中， $\left|\stackrel{\to }{AB}\right|+\left|\stackrel{\to }{BD}\right|+\left|\stackrel{\to }{DC}\right|=4,\stackrel{\to }{AB}·\stackrel{\to }{BD}=\stackrel{\to }{BD}·\stackrel{\to }{DC}=O$, $\left|\stackrel{\to }{AB}\right|·\left|\stackrel{\to }{BD}\right|+\left|\stackrel{\to }{BD}\right|·\left|\stackrel{\to }{DC}\right|=4$，则 $(\stackrel{\to }{AB}+\stackrel{\to }{DC})·\stackrel{\to }{AC}$的值为（   ）

A．

2

B．

$2\sqrt{2}$

C．

4

D．

$4\sqrt{2}$