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What is the circumference of the circle above with center O?

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What is the circumference of the circle above with center O? [#permalink] New post 26 Dec 2012, 03:59
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What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is 20 + 10\sqrt{2}.
(2) The length of arc XYZ is 5\pi.
[Reveal] Spoiler: OA
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Re: What is the circumference of the circle above with center O? [#permalink] New post 26 Dec 2012, 04:05
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Image
What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is 20 + 10\sqrt{2}. Since <O=90 degrees and OX=OZ=r, then XZ=r\sqrt{2}. Thus we have that r+r+r\sqrt{2}=20 + 10\sqrt{2} --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is 5\pi. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = 20\pi. Sufficient.

Answer: D.
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Re: What is the circumference of the circle above with center O? [#permalink] New post 12 Jan 2013, 07:33
Bunuel wrote:
Image
What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is 20 + 10\sqrt{2}. Since <O=90 degrees and OX=OZ=r, then XZ=r\sqrt{2}. Thus we have that r+r+r\sqrt{2}=20 + 10\sqrt{2} --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is 5\pi. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = 20\pi. Sufficient.

Answer: D.


Is there a formula for this explanation?
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Re: What is the circumference of the circle above with center O? [#permalink] New post 13 Jan 2013, 02:29
Expert's post
fozzzy wrote:
Bunuel wrote:
Image
What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is 20 + 10\sqrt{2}. Since <O=90 degrees and OX=OZ=r, then XZ=r\sqrt{2}. Thus we have that r+r+r\sqrt{2}=20 + 10\sqrt{2} --> we can find r, thus we can find the circumference. Sufficient.

(2) The length of arc XYZ is 5\pi. Again, since <O=90 degrees, then the length of arc XYZ is 1/4 of the circumference (360 degrees), thus the circumference = 20\pi. Sufficient.

Answer: D.


Is there a formula for this explanation?


Yes, check here: math-circles-87957.html (see Arc Length under Arcs and Sectors chapter)
_________________

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: What is the circumference of the circle above with center O?   [#permalink] 13 Jan 2013, 02:29
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