4. As shown in Figure 2, in the Cartesian coordinate system, point $A\left(\cos 110^{\circ}, \sin 110^{\circ}\right)$, $B\left(\cos 50^{\circ}, \sin 50^{\circ}\right)$. The distance from the origin $O$ to the midpoint $M$ of $A B$ is ( ).
(A) $\frac{1}{2}$
(B) $\frac{\sqrt{2}}{2}$
(C) $\frac{\sqrt{3}}{2}$
(D) 1
4. C.

From the given information, we have
$$
\begin{array}{l}
|O A|=1,|O B|=1, \\
\angle A O B=110^{\circ}-50^{\circ}=60^{\circ} .
\end{array}
$$

Thus, $\triangle A O B$ is an equilateral triangle, and $|A B|=1$.
Therefore, the distance from point $O$ to the midpoint $M$ of $A B$ is the length of the altitude of an equilateral triangle with side length 1, which is $\frac{\sqrt{3}}{2}$.