If $C$ is the midpoint of $AB$ and $P$ is any point outside $AB$, then:

Let the position vectors of $A,B$, and $C$ with respect to $P$ be $\overrightarrow{PA},\overrightarrow{PB}$, and $\overrightarrow{PC}$ respectively.Since $C$ is the midpoint of $AB$, its position vector relative to $P$ is given by:
$$\overrightarrow{PC}=\frac{\overrightarrow{PA}+\overrightarrow{PB}}{2}$$
Multiplying by 2:
$$2\overrightarrow{PC}=\overrightarrow{PA}+\overrightarrow{PB}$$
Thus, $\overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC}$.