The variables of circles in x-y coordinates are 3 (center and radii). In order to match the number of numbers to the number of equations, we need 3 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that E is the correct answer. Using both the condition 1) and the condition 2), since AB=2√3=diameter, the answer is always yes, and the condition is sufficient. Therefore, the correct answer is C.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.