$\triangle A B C$ 中, $A C=\sqrt{2}, A B=2, A=45^{\circ}, P$ 是 $\triangle A B C$ 外接圆上一点, $\overrightarrow{A P}=\lambda \overrightarrow{A B}+\mu \overrightarrow{A C}$, 则 $\lambda+\mu$ 的最大值是
A
$\frac{\sqrt{2}+1}{2}$
B
$\frac{\sqrt{2}-1}{2}$
C
$\frac{\sqrt{3}-\sqrt{2}}{2}$
D
$\frac{\sqrt{3}+\sqrt{2}}{2}$
E
F