Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 18 Jun 2013, 14:38
Customize  |  Hide

Search
Register
New posts
Unanswered

A circle inscribed in an equilateral triangle with side

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
TAGS:
SVP
SVP
Joined: 14 Dec 2004
Posts: 1714
Followers: 1

Kudos [?]: 17 [0], given: 0

GMAT Tests User
A circle inscribed in an equilateral triangle with side [#permalink] New post 31 Dec 2005, 23:18
00:00

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
A circle inscribed in an equilateral triangle with side length 20. What is the area of inscribed circle?


No OA available. Just try!
VP
VP
User avatar
Joined: 29 Dec 2005
Posts: 1356
Followers: 6

Kudos [?]: 17 [0], given: 0

GMAT Tests User
Re: PS: Circle in Eqvilateral Triangle [#permalink] New post 31 Dec 2005, 23:27
vivek123 wrote:
A circle inscribed in an equilateral triangle with side length 20. What is the area of inscribed circle?
No OA available. Just try!

draw a triangle by adding the mid point of each side of the equilateral triangle. this new trangle, also equilateral trangle, is inscribed in the circle. the side of the new equi trangle is 10.
so r = a/sqrt 3 = 10/sqrt(3)

Area of the circle = pi (10/sqrt(3))^2 = (100/3) (pi)
Senior Manager
Senior Manager
User avatar
Joined: 05 Jan 2005
Posts: 254
Followers: 1

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

GMAT Tests User
 [#permalink] New post 01 Jan 2006, 17:45
another way to solve this could be...

draw perpendicular bisectors of each angle. They should meet at the centroid of the triangle which is the center of the circle. the radius of the circle is 1/3 the length of the bisector.

or

length of bisector x = [(20)^2-(10)^2]^1/2 = 300^1/2

area = pi*300*1/3*1/3 = 100pi/3
Senior Manager
Senior Manager
User avatar
Joined: 05 Jan 2005
Posts: 254
Followers: 1

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

GMAT Tests User
Re: PS: Circle in Eqvilateral Triangle [#permalink] New post 01 Jan 2006, 17:48
Professor wrote:
vivek123 wrote:
A circle inscribed in an equilateral triangle with side length 20. What is the area of inscribed circle?
No OA available. Just try!

draw a triangle by adding the mid point of each side of the equilateral triangle. this new trangle, also equilateral trangle, is inscribed in the circle. the side of the new equi trangle is 10.
so r = a/sqrt 3 = 10/sqrt(3)

Area of the circle = pi (10/sqrt(3))^2 = (100/3) (pi)



Pls explain "so r = a/sqrt 3" how u got this with working
Senior Manager
Senior Manager
Joined: 11 Nov 2005
Posts: 339
Location: London
Followers: 1

Kudos [?]: 4 [0], given: 0

GMAT Tests User
 [#permalink] New post 01 Jan 2006, 18:09
for a equilateral triangle with side 20, the height of the equilateral triangle is 10sqrt3.

the radius of the inscribed circle within this equilateral traingle is 1/3 of the height of the traingle

so radius is (10sqrt3)/3 = 10/(sqrt3)

area of the inscribed circle = pi* [10/(sqrt3)]^2
= pi*100/3
  [#permalink] 01 Jan 2006, 18:09
    Similar topics Author Replies Last post
Similar
Topics:
 New posts An equilateral triangle is inscribed in a circle. This hallelujah1234 3 11 May 2004, 03:47
New posts A circle is inscribed in an equilateral triangle whose side WinWinMBA 5 01 Jun 2005, 13:10
New posts A circle inscribed in an equilateral triangle with side apollo168 4 20 Aug 2006, 02:07
New posts 1 An equilateral triangle of side 12 is inscribed in a circle mirzohidjon 7 22 Sep 2009, 20:54
New posts Experts publish their posts in the topic An equilateral triangle is inscribed in a circle. If the BN1989 1 11 Apr 2012, 07:58
Display posts from previous: Sort by

A circle inscribed in an equilateral triangle with side

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderators: VeritasPrepKarishma, Bunuel, IanStewart

Search for:


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com