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In the figure above, points A, B, C, 0, and E lie on a line

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In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 14 Dec 2012, 02:31
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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, 0 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
[Reveal] Spoiler: OA
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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 14 Dec 2012, 02:38
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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, 0 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?

We need to find the value of \pi{R^2}-\pi{r^2}, where R is the radius of the larger circle and r is the radius of the smaller circle. So, bascally we need to find R and r.

(1) AB = 3 and BC = 2 --> AB=r=3 and AB+BC=AC=5=R. Sufficient.

(2) CD = 1 and DE = 4 --> CD+DE=CE=R=5. Next, AD+DE=AE=DIAMETER=2R=10, and since AD=2r, then 2r+DE=10 --> 2r+4=10 --> r=3. Sufficient.

Answer: D.
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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 30 Apr 2014, 23:11
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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 14 May 2014, 17:29
Kudos for the solution. I tried to solve the problem twice, but could not get it. I am hoping to start getting solutions to such problems with more practice :-|
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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 31 May 2014, 02:28
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Hi Bunuel, There is a typo in the question stem. What you refer to as point O in question is shown by D in the diagram. FYKI. Thanks!
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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 31 May 2014, 03:22
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In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 01 Jul 2014, 21:55
Bunuel - As we know CE=AC=5 so AD=2r=AC+CD=6, can this be an alternative way to confirm that statement#2 is sufficient?
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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink] New post 05 Jul 2014, 06:35
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Re: In the figure above, points A, B, C, 0, and E lie on a line   [#permalink] 05 Jul 2014, 06:35
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