Data Sufficiency

In the figure above, 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

Please refer the diagram in OG

OA: D


My doubt:

I actually selected A and ignored statement (ii) as insufficient because I thought that i should not trust the diagram without further information. In other words, statement (ii) says that CD=1 and DE=4. From the diagram, we could infer that CE is the radius and therefore CE = CD+DE = 1+4 = 5 (This is what is given in OG-12)

But, i thought that D could be outside the inner circle and could also be inside the inner circle. That is, there could be 2 possibilities

If D is outside the inner circle, then CE = CD+DE = 5 (radius of outer circle)
If D is inside the inner circle, then CE = DE - CD = 3 (radius of outer circle)

For this reason, i ignored B and selected A.

What is wrong in my thought? Did i go beyond the scope of ambiguity in diagrams? If so, why?