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In the xy-plane, point (r, s) lies on a circle with center [#permalink]
06 Feb 2006, 16:51

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 (sqrt2, -sqrt2) lies on the circle.

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 (sqrt2, -sqrt2) lies on the circle.

D. since r2 + s2 is redius^2 and both give the value of redius^2.

Can someone help explain this in a little more detail? Ther must be some property of circles that I am not familiar with...

friend, the key fact of this problem is that the distance from the centre of a circle to any point on the circle is equal to the radius of the circle. Here, the centre is the origin of the coordination plane thus:
the distance from the centre to the provided point =
sqrt [ (r-0)^2 + (s-0)^2] = sqrt (r^2 + s^2)
this distance= the radius ---> sqrt(r^2+s^2) = 2 ---> r^2+s^2= 4

---> stmt 1 is suff

stmt 2 already provides us the measure of the radius ---> back to stmt 1 ---> suff

Ah-
I think I was interpreting the question wrong. It says:

joemama142000 wrote:

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 (sqrt2, -sqrt2) lies on the circle.

Can someone help explain this in a little more detail? Ther must be some property of circles that I am not familiar with...

friend, the key fact of this problem is that the distance from the centre of a circle to any point on the circle is equal to the radius of the circle. Here, the centre is the origin of the coordination plane thus: the distance from the centre to the provided point = sqrt [ (r-0)^2 + (s-0)^2] = sqrt (r^2 + s^2) this distance= the radius ---> sqrt(r^2+s^2) = 2 ---> r^2+s^2= 4

---> stmt 1 is suff

stmt 2 already provides us the measure of the radius ---> back to stmt 1 ---> suff

thnk u , i cld ve picked A , but now i understand. _________________