GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 21 Feb 2020, 02:12

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Circle O is inscribed in equilateral triangle ABC. If the area of ABC

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61358
Circle O is inscribed in equilateral triangle ABC. If the area of ABC  [#permalink]

Show Tags

New post 15 Nov 2019, 00:28
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (02:25) correct 43% (02:34) wrong based on 40 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: Circle O is inscribed in equilateral triangle ABC. If the area of ABC  [#permalink]

Show Tags

New post 17 Nov 2019, 20:51
2
Bunuel wrote:
Circle O is inscribed in equilateral triangle ABC. If the area of ABC is \(24 \sqrt{3}\), what is area of circle O?


A. \(2\pi\sqrt{3}\)

B. \(4\pi\)

C. \(4\pi\sqrt{3}\)

D. \(8\pi\)

E. \(12\pi\)


Are You Up For the Challenge: 700 Level Questions



Area of Equilateral Triangle: (√3/4)*a^2
therefore, (√3/4)*a^2= 24√3; a=4√6

The radius of a circle when inscribed in Equilateral Triangle: r = (√3a )/ 6
r= (√3*4*√6)/6
r= 2√2

Area of circle= pi*r^2
therefore, the area of a circle: pi* (2√2)^2 = 8pi

please provide the kudus :thumbup: :thumbup:
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5888
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: Circle O is inscribed in equilateral triangle ABC. If the area of ABC  [#permalink]

Show Tags

New post 15 Nov 2019, 00:41
side of ∆ = 24√3 = √3*s^2/4
s= 4√6
radius of inscribed circle = s*√3/6
r= 4√6*√3/6
r= 2√18/3
area of circle = pi * ( 2√18/3)^2 = \(8\pi\)
IMO D


Bunuel wrote:
Circle O is inscribed in equilateral triangle ABC. If the area of ABC is \(24 \sqrt{3}\), what is area of circle O?


A. \(2\pi\sqrt{3}\)

B. \(4\pi\)

C. \(4\pi\sqrt{3}\)

D. \(8\pi\)

E. \(12\pi\)


Are You Up For the Challenge: 700 Level Questions
Intern
Intern
avatar
B
Joined: 23 Jan 2020
Posts: 3
Re: Circle O is inscribed in equilateral triangle ABC. If the area of ABC  [#permalink]

Show Tags

New post 13 Feb 2020, 03:00
Since GMAT doesn't really care how we get the answer, I tried approximation here. For those who did not remember the side to radius relations,
Area for triangle= 24*3^1/3 = 40 approx.
Area of an inscribed circle in an equilateral triangle is roughly 60% of the traingles area = 40*3/5 = 24
Of the given options, 8pi is closest to 24 hence
IMO D
GMAT Club Bot
Re: Circle O is inscribed in equilateral triangle ABC. If the area of ABC   [#permalink] 13 Feb 2020, 03:00
Display posts from previous: Sort by

Circle O is inscribed in equilateral triangle ABC. If the area of ABC

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne