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

It is currently 04 Aug 2015, 12:11
GMAT Club Tests

Alert:

GMAT Club Expert Essay Review: Submit Yours Here


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

A circle is inscribed in an isosceles trapezoid with bases 8

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
Joined: 28 Aug 2004
Posts: 205
Followers: 1

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

A circle is inscribed in an isosceles trapezoid with bases 8 [#permalink] New post 09 Oct 2004, 05:31
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:01) correct 0% (00:00) wrong based on 1 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A circle is inscribed in an isosceles trapezoid with bases 8 and 18. What is the area of the circle?

A. 36pi
B. 49pi
C. 64pi
D. 81pi
Manager
Manager
avatar
Joined: 07 Sep 2004
Posts: 60
Followers: 1

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

 [#permalink] New post 09 Oct 2004, 06:22
the answer is A

anyway, I will explain as much as I could

AB and CD are the bases of trapezoid (AB=8 , CD=18)
draw the segment joining the midpoint of AB (M) to midpoint of CD (N)
The center should be the midpoint of MN. I called O.

The circle intersect BC at P
MB=BP=4
PC=CN=9 this implies BC=4+9=13

Notice that MN is a diameter of circle
After dropping the altitude from B to NC, we can know that the altitude is 12.
MN=12 implies radius is 6.

Hope I made it clear but I frankly could not see it as a GMAT question. Took me around 5 minutes.
Senior Manager
Senior Manager
avatar
Joined: 19 May 2004
Posts: 291
Followers: 1

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

 [#permalink] New post 10 Oct 2004, 00:07
Great solution amernassar.
Thanks for the explanation.
Director
Director
User avatar
Joined: 31 Aug 2004
Posts: 610
Followers: 3

Kudos [?]: 58 [0], given: 0

 [#permalink] New post 10 Oct 2004, 07:06
I do not understand how it is possible to find any solution to this pb. We just know bases lengths height of the trapezoid can be 10 or 3000...
Manager
Manager
avatar
Joined: 07 Sep 2004
Posts: 60
Followers: 1

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

 [#permalink] New post 10 Oct 2004, 08:08
The problem says that a circle is inscribed in an isosceles trapezoid which means that there is a restriction of some kind on the trapezoid in order to be true, he is just asking in another way what height would it be for the circle to be inscribed.

Of course a height of 3000 for the isosceles trapezoid could not be circumscribed in any circle,just imagine it.


Another problem let's say. find the area of rectangle of width 5 inscribed in a circle of radius 6.5. Do we say that we have missing information for the length to solve it, or the restriction given to the problem solves the length of the rectangle and thus the problem.


Hope this twixt has helped in some way.
Senior Manager
Senior Manager
avatar
Joined: 19 May 2004
Posts: 291
Followers: 1

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

 [#permalink] New post 10 Oct 2004, 09:02
twixt, i think that this is what you're missing:

From symmetry reasons, a perpendicular from the middle of base AB to the middle of base DC will divide the circle to two equal pieces.
The crucial thing to understand inorder to solve this question, is that MB, which is half of AB and equals to 4, is also equal to BP, where P is the point where the circle touches BC.
Two tangents to a circle from the same point are equal.
Once you find this, the question is easily solved.

I agree that this question seems out of scope!
Manager
Manager
avatar
Joined: 28 Aug 2004
Posts: 205
Followers: 1

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

 [#permalink] New post 10 Oct 2004, 10:11
Equally important is to realize that an altitude from B to NC should be drawn, parallel and equal to the diameter, to form a triangle...then it becomes sort of easy. The difficulty lies in knowing what 'extra' work we have to do the diagram to solve the problem out - in other words, what the stem offers you may be good but not enough!
  [#permalink] 10 Oct 2004, 10:11
Display posts from previous: Sort by

A circle is inscribed in an isosceles trapezoid with bases 8

  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®.