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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]

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21 Sep 2010, 23:05
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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]

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21 Sep 2010, 23:09
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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.

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Re: Does the point P touch the circle? [#permalink]

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22 Sep 2010, 13:36
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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.
Attachments

Circle XY.pdf [3.29 KiB]

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Re: Does the point P touch the circle? [#permalink]

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22 Sep 2010, 13:10
Thanks a lot for the explanation Bunell...
+1
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Re: Does the point P touch the circle? [#permalink]

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22 Sep 2010, 16:21
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]

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30 Jul 2014, 22:18
Hello from the GMAT Club BumpBot!

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Re: A certain circular area has its center at point P and has [#permalink]

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31 Jul 2014, 01:16
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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.

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Re: A certain circular area has its center at point P and has [#permalink]

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21 Jun 2016, 04:56
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Re: A certain circular area has its center at point P and has [#permalink]

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14 Jul 2016, 21:56
vigneshpandi 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.
(2) The distance between point X and point Y is 9.

The answer is an emphatic C

(1) The distance between point P and point X is 4.5.
Since the radius of the circle is 4 every point >4 will lie outside the circle. SO X is definitely outside the circle. BUT THE QUESTION IS ASKING ABOUT Y.
INSUFFICIENT

(2) The distance between point X and point Y is 9
We cannot find out the relative position of X and Y from this statement alone. There is no data at all. Even the question stem is useless.
INSUFFICIENT

Merge both statement

X is 4.5 away from the centre. Since the radius is 4 therefore X will always be 0.5 away from the centre and outside the centre.
Now Y is 9 away from X. Even if we take it to be directly opposite X on the other side of circle on a line that is the diameter of the circle it will be 9-(0.5 +8)= 0.5 away
the circle and hence always outside the circle.

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Re: A certain circular area has its center at point P and has   [#permalink] 14 Jul 2016, 21:56
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# A certain circular area has its center at point P and has

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