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If equilateral triangle MNP is inscribed in circle O with

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If equilateral triangle MNP is inscribed in circle O with [#permalink] New post 31 Mar 2012, 15:46
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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

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Re: Length of Arc MN [#permalink] New post 31 Mar 2012, 15:52
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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.

Answer: B.
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Re: Length of Arc MN [#permalink] New post 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.

Answer: B.


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.
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Re: Length of Arc MN [#permalink] New post 01 Apr 2012, 15:12
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.

Answer: B.


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..
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If equilateral triangle MNP is inscribed in circle O with [#permalink] New post 13 Nov 2013, 14:59
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Re: If equilateral triangle MNP is inscribed in circle O with   [#permalink] 13 Nov 2013, 14:59
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