Circle $\odot O$ has radius 1. Line $PA$ is tangent to $\odot O$ at point $A$. Line $PB$ intersects $\odot O$ at points $B$ and $C$. $D$ is the midpoint of $BC$. If $| P O | = \sqrt { 2 }$, then the maximum value of $\overrightarrow { P A } \cdot \overrightarrow { P D }$ is\\
A. $\frac { 1 + \sqrt { 2 } } { 2 }$\\
B. $\frac { 1 + 2 \sqrt { 2 } } { 2 }$\\
C. $1 + \sqrt { 2 }$\\
D. $2 + \sqrt { 2 }$