3. In Rt $\triangle A B C$, $\angle C=90^{\circ}, A C>B C$. $D$ is a point on side $A C$ ( $D$ does not coincide with $A$ or $C$), and satisfies $C D \cdot C A>C B^{2}$. A line $l$ is drawn through point $D$ to intersect $\triangle A B C$, such that the intersected triangle is similar to $\triangle A B C$. Then the number of lines $l$ that satisfy the condition is ( ) lines.
(A) 1
(B) 2
(C) 3
(D) 4
3.C.

There are 3 lines $l$ that satisfy the conditions. As shown in Figure 5(a), among them, $l_{1} / / B C, l_{2} \perp A B, l_{3} / / A B$.
Figure 5
Note: If the line $l_{4}$ passing through point $D$ forms an acute angle $\alpha$ with $D C$ equal to $\angle B$, it does not intersect side $C B$, but intersects the extension of side $C B$. The reason is as follows:
Assume $l_{4}$ intersects line $C B$ at point $E$. Then
$\triangle E D C \backsim \triangle A B C$
$\Rightarrow C D \cdot C A=C B \cdot C E$.
Given that $C D \cdot C A>C B^{2}$, thus, $C E>C B$.
Therefore, point $E$ is on the extension of side $C B$ (as shown in Figure 5(b)). Hence, line $l_{4}$ does not satisfy the conditions.