Last visit was: 13 Dec 2024, 19:50 It is currently 13 Dec 2024, 19:50
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
mmelendez
User avatar
Joined: 10 Oct 2012
Last visit: 12 Jul 2020
Posts: 23
Own Kudos:
100
 []
Given Kudos: 22
Posts: 23
Kudos: 100
 []
In the figure AB and CD Updated on: 12 Nov 2015, 13:10
Originally posted by mmelendez on 12 Nov 2015, 10:18.
Last edited by mmelendez on 12 Nov 2015, 13:10, edited 1 time in total.
3
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

50% (02:53) correct 50% (02:50) wrong based on 22 sessions

History

Date
Time
Result
Not Attempted Yet
In the figure, AB and CD are diameters of the circle with center O and AB bisects CD, and chord DF intersects AB at E. if DE=6 and EF=2, Then the area of the circle is?

A 23π
B 47π/2
C 24π
D 49π/2
E 25π

Kudos if you like the question



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
C
User avatar
mmelendez
User avatar
Joined: 10 Oct 2012
Last visit: 12 Jul 2020
Posts: 23
Own Kudos:
100
Given Kudos: 22
Posts: 23
Kudos: 100
In the figure AB and CD 12 Nov 2015, 10:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kudos if you like my question!!!

I will be providing 700 level questions with incredible gmat like thinking skills to solve them.


Enjoy
avatar
bhaskar438
avatar
Joined: 01 Jan 2015
Last visit: 30 Apr 2023
Posts: 54
Own Kudos:
498
Given Kudos: 14
Posts: 54
Kudos: 498
In the figure AB and CD 12 Nov 2015, 20:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mmelendez
kudos if you like my question!!!

I will be providing 700 level questions with incredible gmat like thinking skills to solve them.


Enjoy

I like this question, but my answer choice doesn't match any of the choices; I am getting \(area=\frac{64\pi}{3}.\) What is the source of this question?
User avatar
mmelendez
User avatar
Joined: 10 Oct 2012
Last visit: 12 Jul 2020
Posts: 23
Own Kudos:
100
Given Kudos: 22
Posts: 23
Kudos: 100
In the figure AB and CD 12 Nov 2015, 20:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bhaskar438
mmelendez
kudos if you like my question!!!

I will be providing 700 level questions with incredible gmat like thinking skills to solve them.


Enjoy

I like this question, but my answer choice doesn't match any of the choices; I am getting \(area=\frac{64\pi}{3}.\) What is the source of this question?

Dear bhaskar438

thank you for enjoying this question. I will be posting shortly the explanation. You should follow me as I will be sharing daily only 700 level PS gmat questions.
Please post your work. In 48 hours I will be posting the explanation
avatar
Psiva00734
avatar
Joined: 19 Jan 2015
Last visit: 04 Oct 2017
Posts: 64
Own Kudos:
76
 []
Given Kudos: 1,169
Status:single
Location: India
GPA: 3.2
WE:Sales (Pharmaceuticals and Biotech)
Posts: 64
Kudos: 76
 []
In the figure AB and CD 12 Nov 2015, 22:38
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Both AB and CD are diameters of circle .
so OA=OB=OC=OD=r radius of the circle.
In circles have a property if two chords bisect each other
we can multiply bisect portion each chord.
Here DF chord bisects AB
so DE*EF=AE*EB.

DE=6, EF=2 so AE*EB=12.

AE= AO+OE
EB= OB-OE . Take OA=x, OE=y.
OA=OB radius of the circle. then x^2-y^2=12----1

Here right angled triangle DOE at O , DE=6, OD=r radius of the circle so x
then DE^2=OD^2+OE^2
x^2+y^2=36------2

sum bothe equation 1 and 2 then 2x^2=48=> x= 2root6 radius of the circle

Area of circle pi r^2=24pi.
So answer C is correct
avatar
bhaskar438
avatar
Joined: 01 Jan 2015
Last visit: 30 Apr 2023
Posts: 54
Own Kudos:
498
Given Kudos: 14
Posts: 54
Kudos: 498
In the figure AB and CD 13 Nov 2015, 00:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Psiva00734
Both AB and CD are diameters of circle .
so OA=OB=OC=OD=r radius of the circle.
In circles have a property if two chords bisect each other
we can multiply bisect portion each chord.
Here DF chord bisects AB
so DE*EF=AE*EB.

DE=6, EF=2 so AE*EB=12.

AE= AO+OE
EB= OB-OE . Take OA=x, OE=y.
OA=OB radius of the circle. then x^2-y^2=12----1

Here right angled triangle DOE at O , DE=6, OD=r radius of the circle so x
then DE^2=OD^2+OE^2
x^2+y^2=36------2

sum bothe equation 1 and 2 then 2x^2=48=> x= 2root6 radius of the circle

Area of circle pi r^2=24pi.
So answer C is correct

I have never heard of the intersecting chords theorem before your post!
Without considering the circle, Right triangle CFD with median FO and with side DF = 8, and sides CO and OD congruent can have numerous solutions. Two such solutions are CO=OD=\(\sqrt{24}\) with area of circle equal \(area=24\pi\), and CO=OD=\(8/\sqrt{3}\) with area of circle equal \(area=\frac{64\pi}{3}.\)
I partially neglected the impact the circle has in this question. It is the intersecting chords theorem that ensures an unique solution.
Thanks! I learned something new.
User avatar
rohit8865
User avatar
Joined: 05 Mar 2015
Last visit: 12 Dec 2024
Posts: 840
Own Kudos:
908
Given Kudos: 45
Products:
My Reviews
Posts: 840
Kudos: 908
In the figure AB and CD 17 Jul 2016, 07:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mmelendez
In the figure, AB and CD are diameters of the circle with center O and AB bisects CD, and chord DF intersects AB at E. if DE=6 and EF=2, Then the area of the circle is?

A 23π
B 47π/2
C 24π
D 49π/2
E 25π

Kudos if you like the question
Theorem of intersecting chords say DE*EF=DO*OC
6*8=DO*DO
48=2*DO^2
DO(radius)=Sq root 24
area =π*(sq.rt 24)^2
=24π
Ans C
User avatar
Mahmud6
User avatar
Retired Moderator
Joined: 10 Mar 2013
Last visit: 22 Feb 2022
Posts: 390
Own Kudos:
855
Given Kudos: 235
Status:The best is yet to come.....
Posts: 390
Kudos: 855
In the figure AB and CD 06 Feb 2017, 18:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Psiva00734
Both AB and CD are diameters of circle .
so OA=OB=OC=OD=r radius of the circle.
In circles have a property if two chords bisect each other
we can multiply bisect portion each chord.
Here DF chord bisects AB
so DE*EF=AE*EB.

DE=6, EF=2 so AE*EB=12.

AE= AO+OE
EB= OB-OE . Take OA=x, OE=y.
OA=OB radius of the circle. then x^2-y^2=12----1

Here right angled triangle DOE at O , DE=6, OD=r radius of the circle so x
then DE^2=OD^2+OE^2
x^2+y^2=36------2

sum bothe equation 1 and 2 then 2x^2=48=> x= 2root6 radius of the circle

Area of circle pi r^2=24pi.
So answer C is correct


x^2-y^2=12----1 How?
Would you please explain in details?

Bunuel, would you help us?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderators:
Bunuel
Math Expert
97874 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3116 posts