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

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Re: Does the point P touch the circle? [#permalink]
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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]
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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I3igDmsu 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.

See attached image "Point_Y_Outside_Circle_C2.PNG"

c2 is the circle with radius 4
Q: Is point "Y" outside circle "c2"?

1. Clearly insufficient as it doesn't say a word about point "Y".

It conveys:
If we draw a circle from point p with radius "4.5"(depicted as circle c3), point "X" will somewhere be on this circle and it is definitely outside the circular area(Area within circle c2) mentioned in the stem.

2.
Insufficient.
Attachment:

Point_X_Outside_Or_Inside_c2.PNG [ 10.62 KiB | Viewed 19779 times ]

Combining both;
We know point "X" lies outside the circle c2(radius=4) and it lies on the circle, c3(radius=4.5 and Diameter=9). And point "Y" is 9 units away from point "X". The closest it can ever get to circle c2 will be when it lies on the circle "c3", diagonally opposite to point "X". Just to reiterate, the point "Y" is 9 units away from "X" and 9 is the length of the diagonal of the bigger circle, c3. Thus, point "Y" will never lie on or inside the circle, c2.

Sufficient.

Ans: "C"

Attachment:

Point_Y_Outside_Circle_C2.PNG [ 10.92 KiB | Viewed 19685 times ]
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Re: A certain circular area has its center at point P and has [#permalink]
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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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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.

CORRECT ANSWER IS C
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Re: A certain circular area has its center at point P and has [#permalink]
Hi,

Another way to look at this question

We are told that PX=4.5, and no info about Y so insufficient

We are told that XY is 9 but no info about any relation to circle

Combine 1 and 2 we have

If PXY are not collinear then we have

In Triangle PXY we have PX=4.5, XY=9

Then we have

4.5<PY<13.5
if they are col linear then we have XY is 9 , PX is 4.5 and then we have PY is 4.5 Since PY is more than radius 4 we have P is outside the circle.
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Re: A certain circular area has its center at point P and has [#permalink]
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?

It's probably best to draw here, but you don't need to be overly imaginative to see what's going on anyway.

(1) The distance between point P and point X is 4.5.

This implies that X lies outside the circle. Now, Y can be inside the circle or out, we don't know because the distance b/w X and Y is not given.

Insufficient

(2) The distance between point X and point Y is 9.

Again, same idea we don't know where X and Y stand relative to each other. X can be inside the circle or outside. If it's outside then we can imagine any number of instances where Y is inside. If it's inside, then Y must be outside

Insufficient

C: Now we know that line segment XP is greater than the radius so X exists outside the circle. No matter what, Y will also be outside the circle (the distance b/w X and Y is greater than the diameter).
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Re: A certain circular area has its center at point P and has [#permalink]
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Re: A certain circular area has its center at point P and has [#permalink]
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