It is currently 22 Nov 2017, 04:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Circles inside a circle

Author Message
Manager
Joined: 21 Jul 2009
Posts: 242

Kudos [?]: 138 [0], given: 23

Location: New York, NY

### Show Tags

07 Oct 2009, 16:27
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

86% (00:37) correct 14% (00:00) wrong based on 3 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Three circles of radius 1 are externally tangent to each other and internally
tangent to a larger circle. What is the radius of the larger circle?
Attachment:

untitled.JPG [ 11.06 KiB | Viewed 7033 times ]

Kudos [?]: 138 [0], given: 23

Senior Manager
Joined: 18 Aug 2009
Posts: 318

Kudos [?]: 351 [0], given: 13

Re: Circles inside a circle [#permalink]

### Show Tags

07 Oct 2009, 16:39

The centers of smaller internal circles create an equilateral triangle, with side S = 2.
Intersection point of medians of this triangle lie on the origin/center of the larger circle.
So the radius of the big circle = 2/3*(length of median) + (radius of the smaller circle).
$$R = 2/3*(\sqrt{3}/2)*S + 1 = (2/\sqrt{3}) + 1 = (3 + 2\sqrt{3})/3$$

Kudos [?]: 351 [0], given: 13

Manager
Joined: 21 Jul 2009
Posts: 242

Kudos [?]: 138 [0], given: 23

Location: New York, NY
Re: Circles inside a circle [#permalink]

### Show Tags

08 Oct 2009, 09:28
I don't have an OA, but I'm getting D too.

I put an equilateral triangle with a side of 2 with vertices in the centers of the small circles. The circumcircle of an equilateral triangle is $$\frac{S}{\sqrt{3}}$$, so the distance between the vertices and the center of the large circle is $$\frac{2}{\sqrt{3}}$$. Now add the distance between the vertices to the large circle, which is 1.
$$\frac{2}{\sqrt{3}}+1$$
Which is equal to D.

Kudos [?]: 138 [0], given: 23

Intern
Joined: 02 May 2009
Posts: 21

Kudos [?]: [0], given: 2

Re: Circles inside a circle [#permalink]

### Show Tags

12 Oct 2009, 01:19
hi, agree, i got D as well

Kudos [?]: [0], given: 2

Re: Circles inside a circle   [#permalink] 12 Oct 2009, 01:19
Display posts from previous: Sort by