An equilateral triangle of side 12 is inscribed in a circle : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 10:59

### 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

# An equilateral triangle of side 12 is inscribed in a circle

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 18 Aug 2009
Posts: 435
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 8

Kudos [?]: 121 [0], given: 16

An equilateral triangle of side 12 is inscribed in a circle [#permalink]

### Show Tags

22 Sep 2009, 19:54
10
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

64% (02:33) correct 36% (01:26) wrong based on 108 sessions

### HideShow timer Statistics

An equilateral triangle of side 12 is inscribed in a circle, what is the area of the circle?
[Reveal] Spoiler: OA

Attachments

power.png [ 1.78 KiB | Viewed 3469 times ]

_________________

Never give up,,,

Manager
Joined: 04 Sep 2009
Posts: 52
WE 1: Real estate investment consulting
Followers: 2

Kudos [?]: 23 [1] , given: 7

### Show Tags

23 Sep 2009, 00:32
1
KUDOS
1
This post was
BOOKMARKED
Thanks for the morning warmup!

C - 48P

The height of the triangle equals $$6\sqrt{3}$$ since the sides are 6 and 12 (1:2: \sqrt{3} ratio). So the area of the triangle is $$(6\sqrt{3}*12)/2=36\sqrt{3}$$

Since the triangle is equilateral, we can get 3 equal triangles with area of each $$36\sqrt{3}/2=12\sqrt{3}$$. From this we can get the heights of the smaller triangles: $$12\sqrt{3}*2/12=2\sqrt{3}$$. Thus, the radius is $$6\sqrt{3}-2\sqrt{3}=4\sqrt{3}$$. The area of the cirle is $$(2\sqrt{3})^2*P=48P$$
Senior Manager
Joined: 31 Aug 2009
Posts: 419
Location: Sydney, Australia
Followers: 8

Kudos [?]: 277 [0], given: 20

### Show Tags

23 Sep 2009, 05:18
Was racking my brain on this one. Nice solution arkadiyua.
Manager
Joined: 27 Oct 2008
Posts: 185
Followers: 2

Kudos [?]: 144 [0], given: 3

### Show Tags

23 Sep 2009, 10:29
Soln. I too go with the Ans C - 48pi
Intern
Joined: 17 Aug 2009
Posts: 10
Followers: 0

Kudos [?]: 12 [0], given: 0

### Show Tags

30 Sep 2009, 13:11

I need your help. What do you mean by "we can get 3 equal triangles with area of each..."? I am lost in how to get this three triangles.

Since the triangle is equilateral, we can get 3 equal triangles with area of each $$36\sqrt{3}/2=12\sqrt{3}$$.
Senior Manager
Joined: 31 Aug 2009
Posts: 419
Location: Sydney, Australia
Followers: 8

Kudos [?]: 277 [0], given: 20

### Show Tags

30 Sep 2009, 15:28
konayuki wrote:

I need your help. What do you mean by "we can get 3 equal triangles with area of each..."? I am lost in how to get this three triangles.

Since the triangle is equilateral, we can get 3 equal triangles with area of each $$36\sqrt{3}/2=12\sqrt{3}$$.

If you draw a line from the centre of the circle to each of the triangle vertices you will see that the triangle is divided into 3 equal triangles. In fact if you just draw a triangle… and draw a line from the centre to each of the vertices that will have the same result.

Helps to draw and visualise it.
Intern
Joined: 17 Aug 2009
Posts: 10
Followers: 0

Kudos [?]: 12 [0], given: 0

### Show Tags

30 Sep 2009, 15:48
Thank you! I got it now.
Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 270
Followers: 43

Kudos [?]: 1058 [0], given: 48

### Show Tags

29 Feb 2012, 12:24
4
This post was
BOOKMARKED
remember these formulae for equilateral triangles and you'll save important seconds.
s = side

area of equilateral triangle = $$\frac{s^2}{4}\sqrt{3}$$, height = $$\frac{s}{2}\sqrt{3}$$

radius of circumscribe circle = $$\frac{s}{\sqrt{3}}$$, radius of circumscribe circle = $$\frac{s}{2\sqrt{3}}$$

radius of circle = $$\frac{12}{\sqrt{3}} = 4\sqrt{3}$$ .... s=12

area of circle = $$48\pi$$
_________________

press +1 Kudos to appreciate posts

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13521
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: An equilateral triangle of side 12 is inscribed in a circle [#permalink]

### Show Tags

29 Apr 2016, 14:03
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: An equilateral triangle of side 12 is inscribed in a circle   [#permalink] 29 Apr 2016, 14:03
Similar topics Replies Last post
Similar
Topics:
10 An equilateral triangle is inscribed in a circle. If the 5 11 Apr 2012, 06:58
6 If equilateral triangle MNP is inscribed in circle O with 5 31 Mar 2012, 15:46
1 164 Equilateral triangle is inscribed in a circle. If length 4 05 Mar 2011, 07:50
20 A Circle inscribed in a equilateral triangle ABC so that poi 21 01 Dec 2009, 11:01
5 Circle O is inscribed in equilateral triangle ABC. If the ar 10 21 Sep 2009, 09:19
Display posts from previous: Sort by