Example 3. In the right trapezoid $A B C D$, $A B = 7, A D = 2, B C = 3$. Find the point $P$ on $B A$ such that the triangle with vertices $P, A, D$ is similar to the triangle with vertices $P, B, C$. How many such points $P$ are there?
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(198, Junior High School Competition)
Let $A P=x$, then $P B=7-x$,
(1) If $\triangle P A D \sim \triangle A P B$, then $\frac{x}{7-x}=\frac{2}{3}$.

Solving it, we get $x=\frac{14}{5}<7$. Suitable.
(2) If $\triangle P A D \sim \triangle C B P$, then
$$
\begin{array}{l}
\frac{x}{3}=\frac{2}{7-x}, \\
\therefore x_{1}=6, x_{2}=1
\end{array}
$$

Both satisfy the conditions, so the answer should be (C)