If equilateral triangle MNP is inscribed in circle O with : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 Feb 2017, 19:22

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If equilateral triangle MNP is inscribed in circle O with

Author Message
TAGS:

Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 536
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 75

Kudos [?]: 3069 [1] , given: 217

If equilateral triangle MNP is inscribed in circle O with [#permalink]

Show Tags

31 Mar 2012, 15:46
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

70% (01:00) correct 30% (01:06) wrong based on 133 sessions

HideShow timer Statistics

If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?

(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
Joined: 02 Sep 2009
Posts: 37108
Followers: 7254

Kudos [?]: 96541 [1] , given: 10753

Re: Length of Arc MN [#permalink]

Show Tags

31 Mar 2012, 15:52
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
enigma123 wrote:
If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?
(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?

Since triangle MNP is equilateral each of the 3 minor arcs (MN, NP, PM) will equal to 1/3rd of the circumference, which is $$2\pi{r}=12\pi$$. Hence, the length of minor arc MN is $$\frac{12\pi}{3}=4\pi$$.

_________________
Current Student
Joined: 30 Apr 2011
Posts: 15
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: Length of Arc MN [#permalink]

Show Tags

01 Apr 2012, 14:18
Bunuel wrote:
enigma123 wrote:
If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?
(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?

Since triangle MNP is equilateral each of the 3 minor arcs (MN, NP, PM) will equal to 1/3rd of the circumference, which is $$2\pi{r}=12\pi$$. Hence, the length of minor arc MN is $$\frac{12\pi}{3}=4\pi$$.

I understand the answer, but was initially thrown off by calculating that each triangle angles is 60 degrees and circumference is 12 pi so 60/360 * 12pi = 2pi. What's wrong with this reasoning? Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 37108
Followers: 7254

Kudos [?]: 96541 [1] , given: 10753

Re: Length of Arc MN [#permalink]

Show Tags

01 Apr 2012, 15:12
1
KUDOS
Expert's post
bohdan01 wrote:
Bunuel wrote:
enigma123 wrote:
If equilateral triangle MNP is inscribed in circle O with radius of 6, what is the length of minor arc MN?
(A) 2 pi
(B) 4 pi
(C) 6 pi
(D) 8 pi
(E) 12 pi

How come the answer is B guys?

Since triangle MNP is equilateral each of the 3 minor arcs (MN, NP, PM) will equal to 1/3rd of the circumference, which is $$2\pi{r}=12\pi$$. Hence, the length of minor arc MN is $$\frac{12\pi}{3}=4\pi$$.

I understand the answer, but was initially thrown off by calculating that each triangle angles is 60 degrees and circumference is 12 pi so 60/360 * 12pi = 2pi. What's wrong with this reasoning? Thank you.

The angle in the formula you are using should be a central angle and 60 degrees angle is inscribed angle.

Now, according to the central angle theorem the measure of inscribed angle is always half the measure of the central angle.. So, the corresponding central angles would be 2*60=120 degrees and if we put this value in your formula we'll get 120/360*12pi=4pi, which is a correct answer.

For more on this subject check Circles chapter of Math Book: math-circles-87957.html

Hope it helps..
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13957
Followers: 590

Kudos [?]: 167 [0], given: 0

Re: If equilateral triangle MNP is inscribed in circle O with [#permalink]

Show Tags

13 Nov 2013, 14:59
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 Legend
Joined: 09 Sep 2013
Posts: 13957
Followers: 590

Kudos [?]: 167 [0], given: 0

Re: If equilateral triangle MNP is inscribed in circle O with [#permalink]

Show Tags

08 Jul 2016, 04:14
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.
_________________
Re: If equilateral triangle MNP is inscribed in circle O with   [#permalink] 08 Jul 2016, 04:14
Similar topics Replies Last post
Similar
Topics:
1 Equilateral triangle ABC is inscribed in a circle with center O, as sh 3 07 Feb 2016, 09:32
8 If circle O is inscribed inside of equilateral triangle T, w 5 12 Jan 2014, 19:19
12 Circle O is inscribed in equilateral triangle ABC. If the 8 18 Nov 2012, 14:16
10 An equilateral triangle is inscribed in a circle. If the 5 11 Apr 2012, 06:58
5 Circle O is inscribed in equilateral triangle ABC. If the ar 10 21 Sep 2009, 09:19
Display posts from previous: Sort by