4. In a right trapezoid $A B C D$, it is known that $A B \perp B C$, $B C / / A D, A B=12, B C=10, A D=6, F$ is a moving point on a circle with center at point $C$ and a radius of 8, $E$ is a point on $A B$. When the value of $D E+E F$ is minimized, the length of $A E$ is ( ).
(A) 4
(B) 4.5
(C) 5
(D) 5.5
4. B.

As shown in Figure 3, extend $DA$ to point $P$ such that $PA = AD = 6$.
Connect $PC$, intersecting $AB$ and $\odot C$ at points $E$ and $F$ respectively, and draw $PQ \perp BC$ at point $Q$.
It is easy to see that the value of $DE + EF$ is minimized.
$$
\begin{array}{l}
\text { From } PC^{2} = PQ^{2} + QC^{2} = AB^{2} + (AD + BC)^{2} \\
= 12^{2} + (6 + 10)^{2} = 20^{2} \\
\Rightarrow PC = 20 . \\
\text { Also, } \triangle BCE \sim \triangle QCP \\
\Rightarrow \frac{BC}{QC} = \frac{BE}{PQ} \Rightarrow \frac{10}{10 + 6} = \frac{BE}{12} \\
\Rightarrow BE = 7.5 \Rightarrow AE = AB - BE = 4.5 .
\end{array}
$$