In the xy-plane a circle C has (0,0) as its center and 5 as

[Max@Math Revolution]

[GMAT math practice question]

In the xy-plane a circle C has (0,0) as its center and 5 as its radius. If line K is tangent to the circle C, what is the equation of line K?

1) Line K is tangent to the circle C at the point (0,5)
2) Line K passes through the point (5,5).

[Max@Math Revolution]

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

If a line is tangent to a circle at a point on the circle, the line is uniquely determined. Thus, condition 1) is sufficient.

Since (5,5) is outside the circle, there are two tangents to the circle passing through this point.
Thus, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A