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In the figure above, points A, B, C, 0, and E lie on a line [#permalink]
14 Dec 2012, 02:31

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

51% (02:26) correct
49% (01:18) wrong based on 265 sessions

Attachment:

Two circles.png [ 5.47 KiB | Viewed 3285 times ]

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?

Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink]
14 Dec 2012, 02:38

3

This post received KUDOS

Expert's post

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.

Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink]
30 Apr 2014, 23:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink]
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

Re: In the figure above, points A, B, C, 0, and E lie on a line [#permalink]
31 May 2014, 02:28

1

This post received KUDOS

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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