3. As shown in Figure $1, A B$ is the diameter of semicircle $O$, $A C$ and $A D$ are both chords, and $\angle B A C = \angle C A D$. Therefore, which of the following equations is true? ( ).
(A) $A C^{2}=A B \cdot A D$
(B) $A B \cdot A D>A C^{2}$
(C) $A B+A D=2 A C$
(D) $A B+A D<2 A C$
3.D.

As shown in Figure 4, draw $O M \perp A D$ at point $M$, $O M$ intersects $A C$ at point $N$, and connect $O C$. It is easy to see that $O C / / A D$.
Therefore,
$$
\begin{array}{l}
\angle C O N=\angle C O M \\
=\angle O M A=90^{\circ}
\end{array}
$$

It is easy to see that $N C > O C =$
$$
\frac{1}{2} A B, A N > A M = \frac{1}{2} A D \text {. }
$$

Thus, $A B + A D < 2 A C$, and $A B \cdot A D < A C^{2}$.