4. As shown in Figure 17, if $P A = P B, \angle A P B = 2 \angle A C B, A C$ intersects $P B$ at point $D$, and $P B = 4$, $P D = 3$, then $A D \cdot D C$ equals ( )
(A) 6
(B) 7
(C) 12
(D) 16
(2001, National Junior High School Mathematics Competition)
From the problem, we can construct a circle with $P$ as the center and $P A$ as the radius. Let $B P$ intersect the circle at point $E$. Then, by the intersecting chords theorem, we have
$$
A D \cdot D C=B D \cdot D E=7 \text{. }
$$