$20 \cdot 24 P A$ is tangent to $\odot O$ at point $A, A B$ is a chord of $\odot O$. If the radius of $\odot O$ is 1, $P A=1, A B=\sqrt{2}$, then the length of $P B$ is 
(A) 1.
(B) $\sqrt{5}$.
(C) 1 or $\sqrt{5}$.
(D) cannot be determined.
(China Guangzhou, Wuhan, Fuzhou, etc. five cities junior high school mathematics league, 1992)
[Solution] According to the problem, there are two possible positions for $B$.
(1) As shown in Figure (1), it is easy to find that $P B=1$;
(2) As shown in Figure (2), in $\triangle A B P$, $A P=1, A B=\sqrt{2}, \angle B A P=90^{\circ}+45^{\circ}$ $=135^{\circ}$. By the cosine rule, we can find $P B=\sqrt{5}$. Therefore, the answer is $(C)$.