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

It is currently 18 Nov 2019, 15:00

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.

Close

Request Expert Reply

Confirm Cancel

In the figure shown, the radius of the bigger circle is 9

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
In the figure shown, the radius of the bigger circle is 9  [#permalink]

Show Tags

New post 02 Aug 2018, 10:27
10
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (02:37) correct 34% (02:31) wrong based on 41 sessions

HideShow timer Statistics

Attachment:
010818.JPG
010818.JPG [ 14.79 KiB | Viewed 885 times ]


In the figure shown, the radius of the bigger circle is 9 and the triangle is equilateral.
What is the radius of the smaller circle?

A. 1
B. 2
C. 3
D. 4
E. 6

Source: EXperts Global

_________________
You've got what it takes, but it will take everything you've got
Senior Manager
Senior Manager
User avatar
V
Joined: 22 Feb 2018
Posts: 415
Re: In the figure shown, the radius of the bigger circle is 9  [#permalink]

Show Tags

New post 02 Aug 2018, 11:48
2
2
pushpitkc wrote:
Attachment:
The attachment 010818.JPG is no longer available


In the figure shown, the radius of the bigger circle is 9 and the triangle is equilateral.
What is the radius of the smaller circle?

A. 1
B. 2
C. 3
D. 4
E. 6

Source: EXperts Global


OA: C
Attachment:
triangle.PNG
triangle.PNG [ 75.27 KiB | Viewed 840 times ]

\(O_s\) be center of small circle, \(O_b\) be center of big circle.
\(O_sD\) = Radius of small circle=\(r\) , \(O_bB\)=Radius of big circle(R)=\(9\)cm

\(\angle DAO_s= \angle BAO_b =\frac{60^{\circ}}{2}=30^{\circ}\)

that means \(\triangle DAO_s\) and \(\triangle BAO_b\) are \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle.
their sides will be ratio of \(1:\sqrt{3}:2\)

In \(\triangle BAO_b\)
\(AO_b=2O_bB=2*9=18\)
\(AO_b =O_bO_s +O_sA\)
\(O_sA =AO_b-O_bO_s=18-(9+r) =9-r\) [Using \(O_bO_s =R+r =9+r\)]

In \(\triangle DAO_s\)
\(O_sA=2O_sD\)
\(9-r = 2r\)
\(r=\frac{9}{3}=3\)
_________________
Good, good Let the kudos flow through you
Director
Director
User avatar
D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 995
WE: Supply Chain Management (Energy and Utilities)
Re: In the figure shown, the radius of the bigger circle is 9  [#permalink]

Show Tags

New post 03 Aug 2018, 02:22
pushpitkc wrote:

In the figure shown, the radius of the bigger circle is 9 and the triangle is equilateral.
What is the radius of the smaller circle?

A. 1
B. 2
C. 3
D. 4
E. 6

Source: EXperts Global


In-radius of equilateral triangle, OG=OD=\(\frac{a}{2\sqrt{3}}\) (Where 'a' is the side of equilateral triangle)
So, GD=2*OG=\(\frac{a}{\sqrt{3}}\)

AD=height of equilateral triangle=\(\sqrt{3}a/2\)

We have AG=AD-GD=\(\sqrt{3}a/2\)-\(\frac{a}{\sqrt{3}}\)=\(\frac{a}{2\sqrt{3}}\)
Or, \(AG=\frac{1}{3}AD\)
Or, AG=1/3(AG+18)
Or, AG=9

Refer the enclosed figure, AEF is an equilateral triangle with center \(O^'\), So, \(O^'G=in-radius=\frac{1}{3}*AG=\frac{1}{3}*9=3\)

Ans. (C)
Attachments

2 circles.JPG
2 circles.JPG [ 27.22 KiB | Viewed 727 times ]

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13604
Re: In the figure shown, the radius of the bigger circle is 9  [#permalink]

Show Tags

New post 21 Oct 2019, 21:29
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.
_________________
GMAT Club Bot
Re: In the figure shown, the radius of the bigger circle is 9   [#permalink] 21 Oct 2019, 21:29
Display posts from previous: Sort by

In the figure shown, the radius of the bigger circle is 9

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne