A circle inscribed in an equilateral triangle with side : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 11:52

### 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

# A circle inscribed in an equilateral triangle with side

Author Message
Senior Manager
Joined: 14 Jul 2006
Posts: 281
Followers: 1

Kudos [?]: 1 [0], given: 0

A circle inscribed in an equilateral triangle with side [#permalink]

### Show Tags

20 Aug 2006, 01:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A circle inscribed in an equilateral triangle with side length 10. What is the area of inscribed circle?
CEO
Joined: 20 Nov 2005
Posts: 2911
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 24

Kudos [?]: 273 [0], given: 0

### Show Tags

20 Aug 2006, 01:18
25PI/3

When the perpendiculars are dropped from the vertices of the triangles then they meet at the centroid of the circle and the centroid will co-incide with the center of the circle. The ratio of length of line from vertex to centroid to line from centroid to side is 2:1.

So length of perpendicular = √(100-25) = 5*√3
Radius of circle = (5*√3)/3 = 5/√3
Area = 25PI/3
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Joined: 14 Jul 2006
Posts: 281
Followers: 1

Kudos [?]: 1 [0], given: 0

### Show Tags

20 Aug 2006, 01:22
Hi PS_dahiya

Your answer to this one coincides with the question bank's. What do you mean when you say centroid?
CEO
Joined: 20 Nov 2005
Posts: 2911
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 24

Kudos [?]: 273 [0], given: 0

### Show Tags

20 Aug 2006, 01:31
apollo168 wrote:
Hi PS_dahiya

Your answer to this one coincides with the question bank's. What do you mean when you say centroid?

In the figure attached. meeting point of the three perpendiculars is the centroid.
Attachments

Triangle.JPG [ 5.16 KiB | Viewed 776 times ]

_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Joined: 14 Jul 2006
Posts: 281
Followers: 1

Kudos [?]: 1 [0], given: 0

### Show Tags

20 Aug 2006, 01:36
Oh I get it. So the lower two triangles created are two 30-60-90 triangles so from there you can solve for the radius. Thanks for the diagram
20 Aug 2006, 01:36
Display posts from previous: Sort by