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# In the xy-plane, point (r, s) lies on a circle with center

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Manager
Joined: 14 Jan 2006
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Schools: HKUST
In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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23 Sep 2008, 12:56
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In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of
r2 + s2?
(1) The circle has radius 2.
(2) The point (v2, -v2) lies on the circle.
Senior Manager
Joined: 31 Jul 2008
Posts: 289
Re: GMAT SET 19 - 3 [#permalink]

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23 Sep 2008, 13:39
was there a figure with one ?

coz whats v2 ??

to mee A
Director
Joined: 23 May 2008
Posts: 799
Re: GMAT SET 19 - 3 [#permalink]

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23 Sep 2008, 14:41
do you mean r^2 + s^2 ? if so I think A
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Posts: 1346
Re: GMAT SET 19 - 3 [#permalink]

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23 Sep 2008, 15:13
Yes, I'm sure the question is asking for r^2 + s^2. If the circle has centre at the origin, then for every point (r, s) on the circle, r^2 + s^2 = radius^2; that just comes from Pythagoras. Each statement gives you the radius, so the answer should be D.
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Joined: 05 Jul 2008
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Re: GMAT SET 19 - 3 [#permalink]

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23 Sep 2008, 16:39
IanStewart wrote:
Yes, I'm sure the question is asking for r^2 + s^2. If the circle has centre at the origin, then for every point (r, s) on the circle, r^2 + s^2 = radius^2; that just comes from Pythagoras. Each statement gives you the radius, so the answer should be D.

How did the second statement ( v2, v-2 ) give us the radius?
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Posts: 1346
Re: GMAT SET 19 - 3 [#permalink]

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24 Sep 2008, 09:10
icandy wrote:
IanStewart wrote:
Yes, I'm sure the question is asking for r^2 + s^2. If the circle has centre at the origin, then for every point (r, s) on the circle, r^2 + s^2 = radius^2; that just comes from Pythagoras. Each statement gives you the radius, so the answer should be D.

How did the second statement ( v2, v-2 ) give us the radius?

You have the co-ordinates of both a point on the circle and the centre of the circle. The distance between them is the radius... I should add that I'm interpreting the notation "( v2, -v2 )" to mean:

$$( \sqrt{2}, - \sqrt{2})$$

which I'm guessing is what is intended. If the 'v' is actually some kind of variable here, then of course we don't have the co-ordinates of a point.
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Re: GMAT SET 19 - 3   [#permalink] 24 Sep 2008, 09:10
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# In the xy-plane, point (r, s) lies on a circle with center

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