To make the solution easier to follow, let's replace (r, s) with (a, b):
jkwan wrote:In the xy-plane, point (a, b) lies on a circle with center at the origin. What is the value of a² + b²?
(1) The circle has radius 2.
(2) The point (√2, -√2) lies on the circle.
The equation for a circle centered at the origin is x² + y² = r², where r is the radius.
Since (a, b) lies on the circle, we get:
a² + b² = r².
Thus, to determine the value of a² + b², we need to know the value of r.
Question rephrased:
What is the value of r?
Statement 1: The circle has radius 2.
SUFFICIENT.
Statement 2: The point (√2, -√2) lies on the circle.
Since the radius is equal to the distance between the origin and any point on the circle -- including (√2, -√2) -- the value of r can be determined.
SUFFICIENT.
The correct answer is
D.
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