3. In $\triangle A B C$, $\angle C=90^{\circ}$, point $D$ is on side $A B$, and $C D^{2}=A D \cdot D B$. Then the position of point $D$ exists in ( ) cases.
(A) 1
(B) 2
(C) 3
(D) infinitely many
3. B.

As shown in Figure 2, draw $C D^{\prime} \perp$ $A B$ at $D^{\prime}$.

Let $A D=a, D D^{\prime}=$ $b, D^{\prime} B=c$. Therefore, we have
$$
\begin{aligned}
& C D^{2}-C D^{\prime 2} \\
= & a(b+c)-(a+b) c \\
= & b(a-c)=D D^{\prime 2}=b^{2} .
\end{aligned}
$$

Thus, $b(a-c)-b^{2}=0$, which gives $b(a-b-c)=0$.
(1) When $b=0$, $D$ coincides with $D^{\prime}$;
(2) When $a=b+c$, $D$ is the midpoint of $A B$. Therefore, there are 2 possible positions for point $D$.