Which of the following points lies on the circle whose center is at the origin and whose radius is 2 sqrt 3?

(0,6)
(2, sqrt 3)
(2, 2 sqrt 2)
(sqrt 3, sqrt 3)

The equation of a circle is defined by (x – h)² + (y – k)² = r² with the center being at (h, k) and with radius r. So for this circle with the center at (0, 0) and r = 2√3 the equation is x² + y² = 12. 
Then we plug in the ordered pairs:
(0, 6)
0² + 6² = 12
36 ≠ 12

(2, √3)
2² + (√3)² = 12
4 + 3 ≠ 12

(2, 2√2)
2² + (2√2)² = 12
4 + 8 = 12

So the answer is (2, 2√2). Hope that helps.