NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 18:12 It is currently 24 Apr 2024, 18:12
Decision Tracker
My Rewards
New posts
New comers' posts

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

In a circle with centre O and radius 1 cm, an arc AB makes an angle 60

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618816 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 [#permalink] New post   03 Apr 2020, 05:55
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

78% (02:44) correct 22% (03:17) wrong based on 32 sessions
Hide Show timer Statistics

In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then what is the length of OC?


A. \(\sqrt{\frac{\pi}{4}}\)

B. \(\sqrt{\frac{\pi}{6}}\)

C. \(\sqrt{\frac{\pi}{3\sqrt{3}}}\)

D. \(\sqrt{\frac{\pi}{4\sqrt{3}}}\)

E. \(\sqrt{\frac{\pi}{5\sqrt{3}}}\)




Are You Up For the Challenge: 700 Level Questions

Show Spoiler
Attachment:
sector.png
sector.png [ 14.25 KiB | Viewed 3380 times ]
ShowHide Answer
Official Answer
C
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [0]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 [#permalink] New post   03 Apr 2020, 06:40
Area of sector =60/360πr^2
Area of Sector=1/6π=R
Area of Triangle OCD is r/2
∆OCD=1/12π
Also, the area of triangle ocd is √3/4x^2(where x is length of OC)
1/12π=√3/4x^2
X=√(π/3√3)
OA is C

Posted from my mobile device
User avatar
L
AnirudhaS
LBS Moderator
Joined: 30 Oct 2019
Posts: 836
Own Kudos [?]: 775 [0]
Given Kudos: 1577
Send PM
Re: In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 [#permalink] New post   03 Apr 2020, 07:12
Area of region R = \(\pi r^2 * \frac{360}{6}\) = \(\frac{\pi }{6}\) , since r = 1
Now, \(\frac{\pi }{6} * \frac{1}{2}\) = △ OCD
or, △ OCD = \(\frac{\pi }{12}\) .. equation (i)

Now, since OC=OD, so ∠OCD=∠ODC.
Hence, ∠OCD=∠ODC=∠COD=60 deg
Therefore, OC=CD=OD

Now we can equate from equation (i),
△ OCD = \(\frac{\pi }{12}\),
or, \(\frac{\sqrt{3}}{4} * x^2\)= \(\frac{\pi }{12}\)
therefore, x = \(\sqrt{\frac{\pi }{ 3 \sqrt3}}\)
Answer: C
User avatar
D
ArunSharma12
Director
Director
Joined: 25 Oct 2015
Posts: 516
Own Kudos [?]: 879 [0]
Given Kudos: 74
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
Send PM
Reviews Badge
Re: In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 [#permalink] New post   03 Apr 2020, 07:18
Bunuel wrote:

In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then what is the length of OC?


A. \(\sqrt{\frac{\pi}{4}}\)

B. \(\sqrt{\frac{\pi}{6}}\)

C. \(\sqrt{\frac{\pi}{3\sqrt{3}}}\)

D. \(\sqrt{\frac{\pi}{4\sqrt{3}}}\)

E. \(\sqrt{\frac{\pi}{5\sqrt{3}}}\)

[/spoiler]


let the OC be a.

R = \( \frac{\pi *(1)^2*60}{360} \) = \( \frac{\pi }{6} \)
Area of triangle OCD = \(\frac{1*(a)^2*sin(60)}{2}\)= \( \frac{\pi }{6*2} \)
\((a)^2\)=\( \frac{\pi }{6*sin(60)} \)=\( \frac{\pi*2 }{6*\sqrt{3}} \)=\( \frac{\pi }{3*\sqrt{3}} \)
\(a= \sqrt{\frac{\pi}{3\sqrt{3}}}\)
Ans: C
GMAT Club Bot
gmatclubot
Re: In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 [#permalink]
03 Apr 2020, 07:18
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions