[Solution] As shown in Figure (2), the maximum overlapping area is $\frac{2}{9} S$ (refer to the measurement in Figure (1)), where $S$ is the area of the original equilateral triangle.
The minimum overlapping area, as shown in Figure (3), is $\frac{1}{9} S$.
Thus, the ratio of the two areas is $2: 1$.
Therefore, the answer is $(B)$.
$21 \cdot 3$ On a plane, there are two congruent equilateral triangles, one of which has a vertex at the center of the other. Then the ratio of the maximum area of the overlapping part to the minimum area is
(A) 1 .
(B) 2 .
(C) 3 .
(D) 4 .