探讨TT数学2中一题，答案可能有误

marco_polo

[attachimg]63741[/attachimg]
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答案D，我选A

[attachimg]63741[/attachimg]
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答案D，我选A

1）可以得出大圆和小圆的半径，算面积差没问题。2）只能算出大圆的面积，无法直接算出小圆面积。不知道我的想法对不对

dsj2510

设AB=x

BC=x-1

AB+BC=x+x-1=5

x=3

marco_polo

谢谢dsj2510,AB+BC=x+x-1=5这用的是（1）给出的数据，（2）单独并不能得出这个结论

allright

条件二可以得出both 大圆半径R和小圆半径r的

CD=2r-R=1

DE+CD=R=5

则明显r=3

marco_polo

allright的思路是对的，谢谢。