GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 May 2019, 21:19

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

GMAT prep-geometry

Author Message
Intern
Joined: 26 Jan 2009
Posts: 22
Schools: University of Toronto, Schulich, Western, Queens

Show Tags

11 Apr 2009, 15:21
2
00:00

Difficulty:

(N/A)

Question Stats:

87% (01:05) correct 13% (00:01) wrong based on 120 sessions

HideShow timer Statistics

for some reason i can't figure out these triangle inscribed in circle questions.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

Attachments

geo2.jpg [ 17.52 KiB | Viewed 6150 times ]

SVP
Joined: 29 Aug 2007
Posts: 2310

Show Tags

12 Apr 2009, 07:25
Faroughs wrote:
for some reason i can't figure out these triangle inscribed in circle questions.

Area of a triangle = 1/2 (bh)
So stretch b and h as much/long as you can so that bh/2 is max..
The max. h = 1 and b = 1.
Area = 1/2(1x1) = 1/2
_________________
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT
Manager
Joined: 05 Jan 2009
Posts: 68

Show Tags

12 Apr 2009, 10:33
can you please explain how did you find that area will be maximum when h=1 & b=1 but not any other combination?
Manager
Joined: 11 Apr 2009
Posts: 131

Show Tags

12 Apr 2009, 10:55
The max B+h+1 because the radius is given is 1. since one vertex is hte centre of the circle and the other two are on the circle, we get two line segments which are equal to the raduis of the circle and these two segments correspond to the base and the height of the triangle respectively.
hope this helps.
Intern
Joined: 07 May 2009
Posts: 16

Show Tags

10 May 2009, 04:34
for longer but more linear explanation use calculus. first note that any triangle described above can be broken into two "easier" triangles with a hyp of 1, hight of h and a base of (1-h^2)^(0.5).

so the area of the trinagle would be 2 x (1/2)(h)(1-h^2)^(.5). ---- (1)
this is tricky to differenciate, but just take a square (as what ever maximized the area will aslo maximize area squared)
you get h^2 + h^4 = A^2
differenciate and set to zero
2h+4h^3 = 0 follows that h = (1/2) and plug into (1) and you get 1/2
Intern
Joined: 25 Aug 2011
Posts: 19
Concentration: Entrepreneurship, General Management
GMAT Date: 01-31-2012

Show Tags

23 Nov 2011, 07:45
I still do not get it..... can anyone post a image with the circle and its triangle inscribed... Thanks!!
Manager
Joined: 09 Nov 2011
Posts: 112

Show Tags

23 Nov 2011, 08:50
1
First..In this question the triangle is not inscribed in the Circle. "Inscribed" in Planar geometry means the end points of the triangle must touch the circumference of the circle.
In this case:
Imagine a circle with Centre O. There are 2 points on the circle A and B. There you have your triangle, OAB. since OA and OB are the radii of the circle both are equal to 1.
Now we have to find out the maximum possible area of this Triangle.

Area = 1/2 * Base * Height.

If you take OA as the base, we have to find out what is the maximum height possible for this triangle with B on the Circle.
By simple imagination it can be found out that the max hieght is the radius itself, in any other case, the hieght will be less than the radius.

Hence Area = 1/2 * OA * OB.
or 1/2 * 1 * 1
or 1/2
Option B.
_________________
Time to play the game...
Non-Human User
Joined: 09 Sep 2013
Posts: 11017

Show Tags

20 Jul 2017, 07:33
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.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: GMAT prep-geometry   [#permalink] 20 Jul 2017, 07:33
Display posts from previous: Sort by