4. As shown in Figure 1, the diameter $A B=4$, $O$ is the center of the semicircle, and $C$ is any point on the semicircle different from $A$ and $B$. If $P$ is a moving point on the radius $O C$, then the minimum value of $(\boldsymbol{P A}+\boldsymbol{P B}) \cdot \boldsymbol{P C}$ is ( ).
(A) 2
(B) 0
(C) -1
(D) -2
4.D.

Since $O$ is the midpoint of $AB$, we have
$$
\begin{array}{l}
\boldsymbol{P A}+\boldsymbol{P B}=2 \boldsymbol{P O} . \\
\text { Then }(\boldsymbol{P A}+\boldsymbol{P B}) \cdot \boldsymbol{P C}=2 \boldsymbol{P O} \cdot \boldsymbol{P C} \\
=-2|\boldsymbol{P O}| \cdot|\boldsymbol{P C}| .
\end{array}
$$

Given that $|P O|+|P C|=|O C|=2$ is a constant, thus, $(P A+P B) \cdot P C$ achieves its minimum value of -2 if and only if $|P O|=|P C|=1$, i.e., when $P$ is the midpoint of $O C$.