3. In $\triangle A B C$, it is known that $\angle A=2 \angle B, C D$ is the angle bisector of $\angle C$, $A C=16, A D=8$. Then $B C=$
3. 24 .

From $\angle A=2 \angle B$, we know $B C>A C$.
As shown in Figure 5, take a point $E$ on side $B C$ such that $E C=A C$,
and connect $D E$.
Then $\triangle C E D \cong \triangle C A D$
$$
\begin{array}{l} 
\Rightarrow E D=A D, \\
\angle C E D=\angle C A D . \\
\text { Hence } \angle B D E=\angle C E D-\angle D B E \\
= \angle A-\angle B=\angle B=\angle D B E
\end{array}
$$

Therefore, $B E=D E$.
Thus, $B C=B E+C E=A D+A C=8+16=24$.