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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 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, 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 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: Does the point P touch the circle?   [#permalink] 22 Sep 2010, 15:21
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