10. Let $A_{1}, A_{2}, A_{3}, A_{4}$ be pairwise distinct points in a Cartesian coordinate system. If
$$
\begin{array}{l}
\overrightarrow{A_{1} A_{3}}=\lambda \overrightarrow{A_{1} A_{2}}(\lambda \in \mathbf{R}), \\
\overrightarrow{A_{1} A_{4}}=\mu \overrightarrow{A_{1} A_{2}}(\mu \in \mathbf{R}),
\end{array}
$$

and $\frac{1}{\lambda}+\frac{1}{\mu}=2$, then the points $A_{3}, A_{4}$ are said to harmonically divide the points $A_{1}, A_{2}$. Given that points $C, D$ harmonically divide points $A, B$, which of the following statements is correct? ( ).
(A) $C$ could be the midpoint of segment $A B$
(B) $D$ could be the midpoint of segment $A B$
(C) Points $C, D$ could simultaneously lie on segment $A B$
(D) Points $C, D$ cannot simultaneously lie on the extension of segment $A B$