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A certain circular area has its center at point P and has

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A certain circular area has its center at point P and has [#permalink] New post 21 Sep 2010, 22:05
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A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5.
(2) The distance between point X and point Y is 9.
[Reveal] Spoiler: OA

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Re: Does the point P touch the circle? [#permalink] New post 22 Sep 2010, 12:36
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Correct answer is C. We need to use both (1) and (2).
See the attached figure. A little out of proportion, but you will get the idea.
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Circle XY.pdf [3.29 KiB]
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Re: Does the point P touch the circle? [#permalink] New post 21 Sep 2010, 22:09
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A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5. No info about y. Not sufficient.
(2) The distance between point X and point Y is 9. No relationship between this line segment and circle. Not sufficient.

(1)+(2) From (1) X is outside the circle (as radius is 4). Closest point of this circle to the point X equals to 4.5-4=0.5 and the furthest equals to 0.5+8(diameter)=8.5. As XY=9, then Y must be outside the circle. Sufficient.

Answer: C.
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Re: Does the point P touch the circle? [#permalink] New post 22 Sep 2010, 12:10
Thanks a lot for the explanation Bunell...
+1
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Re: Does the point P touch the circle? [#permalink] New post 22 Sep 2010, 15:21
Thank you very much for the diagram....
this helps clearly...
I was using a horrible diagram to solve this problem during exam.... :(
Thanks again +1
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Re: A certain circular area has its center at point P and has [#permalink] New post 30 Jul 2014, 21:18
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Re: A certain circular area has its center at point P and has [#permalink] New post 31 Jul 2014, 00:16
Expert's post
Bunuel wrote:
A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5. No info about y. Not sufficient.
(2) The distance between point X and point Y is 9. No relationship between this line segment and circle. Not sufficient.

(1)+(2) From (1) X is outside the circle (as radius is 4). Closest point of this circle to the point X equals to 4.5-4=0.5 and the furthest equals to 0.5+8(diameter)=8.5. As XY=9, then Y must be outside the circle. Sufficient.

Answer: C.


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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: A certain circular area has its center at point P and has   [#permalink] 31 Jul 2014, 00:16
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