radius

[ketkoag]

Point (r,s) is on a certain circle, (r^2)*(s^2)=?
1) Radius is 2.
2) Point (root2, -root2) is on the circle also.

Please confirm the answer, [spoiler]IMO : E[/spoiler]

[SanjeevK]

IMO [spoiler]E:[/spoiler]
Equation of circle is: (x-h)^2 + (y-k)^2 = r^2
Here h and k are co-ordinates of circle and r is radius.
a: radius is 2. So we have (x-h)^2 + (y-k)^2 = 4.
Point (r,s) lies on the circle. Hence (r-h)^2 + (s-k)^2 = 4. We don't know the value of h and k. So we can't determine the value of r,s. Insufficient

b: Point (root2, -root2) is on the circle also.
(sqrt(2)-h)^2 + (-sqrt(2)-k)^2 = r^2. Doesn't give info about h and k. Insufficient

Combining a and b: (sqrt(2)-h)^2 + (-sqrt(2)-k)^2 = 4. Still not sufficient.

Hope this helps