20-101 As shown in the figure, the ratio of the radii of two concentric circles is 1:3. If $AC$ is the diameter of the larger circle, $BC$ is a chord of the larger circle that is tangent to the smaller circle, and $AB=12$, then the radius of the larger circle is
(A) 13.
(B) 18.
(C) 21.
(D) 24.
(E) 26.
(43rd American High School Mathematics Examination, 1992)
[Solution] Let the center of the concentric circles be $O$, and $BC$ be tangent to the smaller circle at $D$. Connect $OD$, which is the radius of the smaller circle.
We can prove that $AB \parallel OD$, and $\triangle CDO \sim \triangle CBA$.
Thus,
$$
\frac{OD}{AB} = \frac{OC}{AC} = \frac{1}{2},
$$
which means
$$
OD = \frac{1}{2} \cdot AB = \frac{1}{2} \cdot 12 = 6.
$$

Therefore, the radius of the larger circle is $3 \cdot 6 = 18$. Hence, the answer is $(B)$.