Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 14:41

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the greatest possible area of a triangular region

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 28 Jun 2008
Posts: 50
Followers: 0

Kudos [?]: 4 [0], given: 31

What is the greatest possible area of a triangular region [#permalink] New post 13 Jun 2009, 14:18
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

57% (01:06) correct 43% (00:37) wrong based on 8 sessions
Hi guys was wondering if anyone could offer a method for solving this problem:

What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?

A. (square root of 3)/4
B. 1/2
C. pie/4
D. 1
E. square root of 2

Answer: B.
Manager
Manager
avatar
Joined: 28 Jan 2004
Posts: 205
Location: India
Followers: 2

Kudos [?]: 10 [0], given: 4

GMAT Tests User
Re: triangular/circle area problem [#permalink] New post 13 Jun 2009, 17:27
The two sides of the triangle will be 1.The max. are will be when it is a right triangle.
So area will be 1/2 * 1 * 1 = 1/2
Current Student
User avatar
Joined: 03 Aug 2006
Posts: 117
Location: Next to Google
Schools: Haas School of Business
Followers: 4

Kudos [?]: 98 [0], given: 3

GMAT Tests User
Re: triangular/circle area problem [#permalink] New post 14 Jun 2009, 00:15
Ian Stewart, one of the mods had a great explanation for this problem which I had copied and saved for my notes. Here is a cut and paste...and again credit goes to Ian for this.

"Imagine the circle is in the co-ordinate plane, centre O at (0,0). You might as well let one of the points A be at (1,0) (you can rotate the circle to get it there if you need to). Consider OA to be the base of our triangle: b=1.

Now, if (c,d) is the third point in the triangle, then the height will be |d|. To get the largest area we need the largest height, and that clearly happens when (c,d) is (0,1) or (0.-1). So the maximum area is 1*1/2 = 1/2."
Senior Manager
Senior Manager
User avatar
Joined: 07 Jan 2008
Posts: 418
Followers: 3

Kudos [?]: 62 [0], given: 0

GMAT Tests User
Re: triangular/circle area problem [#permalink] New post 14 Jun 2009, 09:44
nookway wrote:
Ian Stewart, one of the mods had a great explanation for this problem which I had copied and saved for my notes. Here is a cut and paste...and again credit goes to Ian for this.

"Imagine the circle is in the co-ordinate plane, centre O at (0,0). You might as well let one of the points A be at (1,0) (you can rotate the circle to get it there if you need to). Consider OA to be the base of our triangle: b=1.

Now, if (c,d) is the third point in the triangle, then the height will be |d|. To get the largest area we need the largest height, and that clearly happens when (c,d) is (0,1) or (0.-1). So the maximum area is 1*1/2 = 1/2."



This is very good solution. My way is more sophisticated. I tried to prove that max happen when the corner of circle-based vertex is 45.
Manager
Manager
avatar
Status: Quant 50+?
Joined: 02 Feb 2011
Posts: 107
Concentration: Strategy, Finance
Schools: Tuck '16, Darden '16
Followers: 1

Kudos [?]: 23 [0], given: 22

Re: triangular/circle area problem [#permalink] New post 02 Oct 2011, 16:36
wooh toughie. I thought equilateral would max area and picked A, good question.
Intern
Intern
avatar
Joined: 13 Jul 2011
Posts: 46
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: triangular/circle area problem [#permalink] New post 02 Oct 2011, 18:51
The area of a triangle is 1/2absinx
In this a=b=1
the maximum for sinx is 1 (Sin90=1)
The area will be 1/2*1*1=1/2
Intern
Intern
avatar
Joined: 05 Sep 2011
Posts: 7
Followers: 0

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

Re: triangular/circle area problem [#permalink] New post 03 Oct 2011, 10:11
Guys please help
Two circle
have same
radius of
unit 1. If
each goes
through the
center of
other
circle, what
is the
common area?

Posted from my mobile device Image
Re: triangular/circle area problem   [#permalink] 03 Oct 2011, 10:11
    Similar topics Author Replies Last post
Similar
Topics:
What is the greatest possible area of a triangular region baileyf16 4 29 Oct 2007, 16:57
What is the greatest possible area of a triangular region bewakoof 16 22 Jul 2007, 20:30
What is the greatest possible area of triangular region with nitinneha 3 04 Apr 2007, 15:52
What is the greatest possible area of a triangular region SimaQ 6 01 Nov 2006, 10:08
What is the greatest possible area of a triangular region mrmikec 9 16 Jun 2006, 17:10
Display posts from previous: Sort by

What is the greatest possible area of a triangular region

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.