$20 \cdot 81$ As shown, the diameter of semicircle $O$ lies on the base $AB$ of trapezoid $ABCD$, and it is tangent to the other three sides $BC, CD, DA$. If $BC=2, DA=3$, then the length of $AB$
(A) is 4.
(B) is 5.
(C) is 6.
(D) cannot be determined.
(China Junior High School Mathematics League, 1994)
[Solution] Connect $O C, O D$. Let the radius of the semicircle $O$ be $r$. Then, in $\triangle A O D$, the sides $A O$ and $D A$ both have heights of $r$, so $A O=D A$.

Similarly, $B O=B C$.
Therefore, $A B=B C+D A=5$.
Hence, the answer is $(B)$.