求助一道gwd数学题！！！以及应不应该相信题目给的图

In the figure, points A, B, C, D, and E lie on a line.  A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle.  What is the area of the region inside the larger circle and outside the smaller circle?

(1)          AB = 3 and BC =2

(2)          CD =1 and DE = 4

       

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

这一张是原图，答案给的是D，但是我觉得条件2明明有两种情况，算出来也不一样。。

这是手残的我画的图

也就是说大圆的圆心可以在小圆外面也可以在里面啊。。所以是不是必须根据题目给的图呢，还是我做错了TAT