Last visit was: 06 Jun 2026, 10:25 It is currently 06 Jun 2026, 10:25
Home
Messages
MBA Fair
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
705-805 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 06 Jun 2026
Posts: 111,116
Own Kudos:
819,134
 [13]
Given Kudos: 106,698
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 111,116
Kudos: 819,134
 [13]
A circle is inscribed in equilateral triangle ABC such that point D 17 Sep 2018, 02:03
1
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

57% (02:50) correct 43% (03:16) wrong based on 82 sessions

History

Date
Time
Result
Not Attempted Yet
A circle is inscribed in equilateral triangle ABC such that point D lies on the circle and on the line segment AC, point E lies on the circle and on the line segment AB, point F lies on the circle and on the line segment BC. If the line segment AB = 6, what is the area of the figure created by AB, AC and minor arc DE?


(A) \(3\sqrt{3}-\frac{9}{4}\pi\)

(B) \(3\sqrt{3}- \pi\)

(C) \(6\sqrt{3}-\pi\)

(D) \(9\sqrt{3}-3\pi\)

(E) \(9\sqrt{3}-2\pi\)
ShowHide Answer
Official Answer
B
User avatar
kritisinghvi
User avatar
Joined: 13 Jun 2017
Last visit: 09 Oct 2019
Posts: 13
Own Kudos:
16
 [3]
Given Kudos: 34
Posts: 13
Kudos: 16
 [3]
A circle is inscribed in equilateral triangle ABC such that point D 17 Sep 2018, 02:17
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A circle is inscribed in equilateral triangle ABC such that point D lies on the circle and on the line segment AC, point E lies on the circle and on the line segment AB, point F lies on the circle and on the line segment BC. If the line segment AB = 6, what is the area of the figure created by AB, AC and minor arc DE?


(A) \(3\sqrt{3}-\frac{9}{4}\pi\)

(B) \(3\sqrt{3}- \pi\)

(C) \(6\sqrt{3}-\pi\)

(D) \(9\sqrt{3}-3\pi\)

(E) \(9\sqrt{3}-2\pi\)
Show more

Posted from my mobile device
Attachments

File comment: Answer B , as solved in attached picture
20180917_121346.jpg
20180917_121346.jpg [ 6.92 MiB | Viewed 3645 times ]

User avatar
thefibonacci
User avatar
Joined: 22 Jan 2014
Last visit: 30 Jan 2019
Posts: 130
Own Kudos:
270
Given Kudos: 212
WE:Project Management (Computer Hardware)
Posts: 130
Kudos: 270
A circle is inscribed in equilateral triangle ABC such that point D 17 Sep 2018, 08:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kritisinghvi
Bunuel
A circle is inscribed in equilateral triangle ABC such that point D lies on the circle and on the line segment AC, point E lies on the circle and on the line segment AB, point F lies on the circle and on the line segment BC. If the line segment AB = 6, what is the area of the figure created by AB, AC and minor arc DE?


(A) \(3\sqrt{3}-\frac{9}{4}\pi\)

(B) \(3\sqrt{3}- \pi\)

(C) \(6\sqrt{3}-\pi\)

(D) \(9\sqrt{3}-3\pi\)

(E) \(9\sqrt{3}-2\pi\)

Posted from my mobile device
Show more

won't this give the area which is outside circle but not shaded in your image? can you kindly explain?
User avatar
kritisinghvi
User avatar
Joined: 13 Jun 2017
Last visit: 09 Oct 2019
Posts: 13
Own Kudos:
16
 [1]
Given Kudos: 34
Posts: 13
Kudos: 16
 [1]
A circle is inscribed in equilateral triangle ABC such that point D 17 Sep 2018, 09:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
thefibonacci
kritisinghvi
Bunuel
A circle is inscribed in equilateral triangle ABC such that point D lies on the circle and on the line segment AC, point E lies on the circle and on the line segment AB, point F lies on the circle and on the line segment BC. If the line segment AB = 6, what is the area of the figure created by AB, AC and minor arc DE?


(A) \(3\sqrt{3}-\frac{9}{4}\pi\)

(B) \(3\sqrt{3}- \pi\)

(C) \(6\sqrt{3}-\pi\)

(D) \(9\sqrt{3}-3\pi\)

(E) \(9\sqrt{3}-2\pi\)

Posted from my mobile device

won't this give the area which is outside circle but not shaded in your image? can you kindly explain?
Show more

Let us say the area outside the circle is K = A(ABC)- A(Circle)

We get K = \(9\sqrt{3}-3\pi\)

Since ABC is an equilateral triangle,

the area of created by AB, AC and minor arc DE = the area of created by AB, BC and minor arc EF = the area of created by BC, AC and minor arc DF.

Thus, to get the area of the shaded region we divide K by 3 (as done in the equation of the image) which gives us \(3\sqrt{3}- \pi\)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,187
Own Kudos:
1,128
Posts: 39,187
Kudos: 1,128
A circle is inscribed in equilateral triangle ABC such that point D 14 Aug 2024, 17:00
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.
Moderator:
Bunuel
Math Expert
111116 posts