$△ABC$中，点$D$在$AB$上，$CD$平方$\angle ACB$．若$\stackrel{\rightharpoonup }{CB}=a$，$\stackrel{\rightharpoonup }{CA}=b$，$\left|a\right|=1$，$\left|b\right|=2$，则$\stackrel{\rightharpoonup }{CD}=$

A．

$\frac{1}{3}a+\frac{2}{3}b$

B．

$\frac{2}{3}a+\frac{1}{3}b$

C．

$\frac{3}{5}a+\frac{4}{5}b$

D．

$\frac{4}{5}a+\frac{3}{5}b$