2 circles

[Lhomme]

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

[Dynamo]

IMO D

statement 1

AB = 3 radius of small circle and

AB + BC = 5 radius of bigger circle ....we can calculate the area....SUFF

statement 2

CD+DE = 5 radius of bigger circle

BC = AB-CD

AB+BC = 5

AB+AB-CD = 5

AB= 3... radius of small circle....SUFF

[Lhomme]

I also think answer should be D.

However, Official Answer is A.

[Dynamo]

why should it be A if we can logically calculate radius using both the options...