Last visit was: 29 Apr 2026, 06:22 It is currently 29 Apr 2026, 06:22
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
605-655 (Medium)|   Geometry|      
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,016
 [18]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,016
 [18]
If DB=2, AC=12, and X is the center of the circle shown as the above f 16 Mar 2017, 01:32
Kudos
Add Kudos
18
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:

45% (medium)

Question Stats:

73% (02:23) correct 27% (02:51) wrong based on 146 sessions

History

Date
Time
Result
Not Attempted Yet
Attachment:
geometry.png
geometry.png [ 3.58 KiB | Viewed 4632 times ]

If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)
ShowHide Answer
Official Answer
C
User avatar
0akshay0
User avatar
Joined: 19 Apr 2016
Last visit: 14 Jul 2019
Posts: 192
Own Kudos:
658
 [2]
Given Kudos: 59
Location: India
Schools: Jindal '20 Kelley '20 Broad '20 Carey '20 Mays '20
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE:Web Development (Computer Software)
Schools: Jindal '20 Kelley '20 Broad '20 Carey '20 Mays '20
GMAT 2: 640 Q49 V28
Posts: 192
Kudos: 658
 [2]
If DB=2, AC=12, and X is the center of the circle shown as the above f 16 Mar 2017, 01:52
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
MathRevolution
Attachment:
geometry.png

If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)
Show more

let XC = r (radius), so XD = r - 2

\(r^2 = (r-2)^2 + 6^2\)

\(r^2 = r^2 - 4r + 4 + 36\)

4r = 40

r = 10

Area = pi * r * r = pi*10*10 = 100pi

Hence option C is correct
Hit Kudos if you liked it 8-)
avatar
giobas
avatar
Joined: 09 Sep 2016
Last visit: 09 Nov 2017
Posts: 32
Own Kudos:
314
 [1]
Given Kudos: 10
Location: Georgia
Concentration: Finance, International Business
GPA: 3.75
WE:Analyst (Finance: Investment Banking)
Posts: 32
Kudos: 314
 [1]
If DB=2, AC=12, and X is the center of the circle shown as the above f 16 Mar 2017, 05:03
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
0akshay0
MathRevolution
Attachment:
geometry.png

If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)

let XC = r (radius), so XD = r - 2

\(r^2 = (r-2)^2 + 6^2\)

\(r^2 = r^2 - 4r + 4 + 36\)

4r = 40

r = 10

Area = pi * r * r = pi*10*10 = 100pi

Hence option C is correct
Hit Kudos if you liked it 8-)
Show more


can you explain why lines are perpendicular?
avatar
adityapareshshah
avatar
Joined: 17 Apr 2016
Last visit: 14 Nov 2017
Posts: 59
Own Kudos:
46
Given Kudos: 254
Posts: 59
Kudos: 46
If DB=2, AC=12, and X is the center of the circle shown as the above f 16 Mar 2017, 09:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
0akshay0
MathRevolution
Attachment:
geometry.png

If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle?

A. \(20π\)
B. \(80π\)
C. \(100π\)
D. \(120π\)
E. \(160π\)

let XC = r (radius), so XD = r - 2

\(r^2 = (r-2)^2 + 6^2\)

\(r^2 = r^2 - 4r + 4 + 36\)

4r = 40

r = 10

Area = pi * r * r = pi*10*10 = 100pi

Hence option C is correct
Hit Kudos if you liked it 8-)
Show more

Hi 0akshay0

Can you explain how did you assume AC parallel to XB.
User avatar
KrishnakumarKA1
User avatar
Joined: 05 Jan 2017
Last visit: 13 Oct 2020
Posts: 398
Own Kudos:
314
Given Kudos: 15
Location: India
Posts: 398
Kudos: 314
If DB=2, AC=12, and X is the center of the circle shown as the above f 17 Mar 2017, 03:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
radius = XA = XB = XC= r
XD = XB-BD = r-2
DA = AC/2 = 12/2 = 6
applying pythagoras theorem in triangle xad we get
r^2 = (r-2)^2 + 36

r^2 = r^2 - 4r +4 +36
r = 10

area = pi *10*10 = 100pi
avatar
giobas
avatar
Joined: 09 Sep 2016
Last visit: 09 Nov 2017
Posts: 32
Own Kudos:
314
Given Kudos: 10
Location: Georgia
Concentration: Finance, International Business
GPA: 3.75
WE:Analyst (Finance: Investment Banking)
Posts: 32
Kudos: 314
If DB=2, AC=12, and X is the center of the circle shown as the above f 17 Mar 2017, 03:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ByjusGMATapp
radius = XA = XB = XC= r
XD = XB-BD = r-2
DA = AC/2 = 12/2 = 6
applying pythagoras theorem in triangle xad we get
r^2 = (r-2)^2 + 36

r^2 = r^2 - 4r +4 +36
r = 10

area = pi *10*10 = 100pi
Show more

how do you know that DA =AC/2 ?
avatar
gvvsnraju@1
avatar
Joined: 03 Jan 2016
Last visit: 09 Dec 2018
Posts: 48
Own Kudos:
20
 [1]
Given Kudos: 83
Location: India
WE:Engineering (Energy)
Posts: 48
Kudos: 20
 [1]
If DB=2, AC=12, and X is the center of the circle shown as the above f 18 Mar 2017, 11:00
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Any Perpendicular Drawn from the Center of the circle to a Chord always bisects the Chord.

So AD=DC=AC/2.

Hope this Helps!!!!!!!!!!


Regards
G V V S Narayana Raju


Give +1 Kudos if u like :-D
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,016
 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,016
 [1]
If DB=2, AC=12, and X is the center of the circle shown as the above f 19 Mar 2017, 18:06
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Attachment:
23.png
23.png [ 5.03 KiB | Viewed 4120 times ]

You get the figure shown above, and according to the Pythagorean Theorem, you get \(r^2=(r-2)^2+6^2=r^2-4r+4+36\), and if you get rid of \(r^2\) on both sides and simplify the equation, from 4r=40, you get r=10. Thus, it becomes the area of the circle, which is \(π10^2=100π\).

The answer is C.
Answer: C
avatar
HoldingMidfield
avatar
Joined: 16 Jun 2018
Last visit: 13 Dec 2019
Posts: 3
Own Kudos:
7
 [2]
Given Kudos: 8
Location: India
GMAT 1: 700 Q47 V38
GMAT 1: 700 Q47 V38
Posts: 3
Kudos: 7
 [2]
If DB=2, AC=12, and X is the center of the circle shown as the above f 20 Jul 2018, 22:01
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The solution assumes that line XB is perpendicular to line AC.

Can we assume that 2 lines are perpendicular without any information provided by the question?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,985
Own Kudos:
1,119
Posts: 38,985
Kudos: 1,119
If DB=2, AC=12, and X is the center of the circle shown as the above f 13 Nov 2023, 09:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109968 posts
Krunaal
Tuck School Moderator
852 posts