The answer is D

Since r,s lies on the circle with center at origin, distance between the point and center is the radius. root ((r-0)^2+(s-0)^2) = root(r^2+s^2)

Statement 1 - Radius is 2. We can determine r^2+s^2. Sufficient

Statement 2 - The point (2^1/2 , -2^1/2) lies on the circle. The distance between this point and the center is equal to the distance between R,S and the center. Sufficient.

This is a rephrasing question.

You can simply rephrase it to, What is radius of the circle having center at origin?

1)Radius is 2
if we draw perpendicular from point (r,s) x-intercept would be r and y-intercept would be s.

r^2+s^2 would be square of the hypotenuse which happens to be the radius. i.e. 2^2 = 4.

SUFFICIENT

2)The point (2^1/2 , -2^1/2) lies on the circle
Let us consider this point as (u,v). Again, drawing perpendiculars, we get the x & y intercept both of which have value = 2^(1/2)

Again, hypotenuse is the radius which will remain same whether it is this point or (r,s).

so,r^2+s^2 = (2^(1/2))^2+(2^(1/2))^2=4

SUFFICIENT