Line M is tangent to a circle, which is centered on point

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Source: Veritas Prep

Line M is tangent to a circle, which is centered on point (3, 4). Does Line M run through the point (6, 6)?

1) Line M runs through the point (-8, 6).
2) Line M is tangent to the circle at point (3, 6).

OA B

[GMATGuruNY]

Source: Veritas Prep

Line M is tangent to a circle, which is centered on point (3, 4). Does Line M run through the point (6, 6)?

1) Line M runs through the point (-8, 6).
2) Line M is tangent to the circle at point (3, 6).

Statement 1:
Case 1:

In this case, the answer to the question stem is YES.

Case 2:

In this case, the answer to the question stem is NO.
INSUFFICIENT.

Rule:
A line tangent to a circle and a radius drawn to the point of tangency are PERPENDICULAR.

Statement 2:

As shown in the figure above, the radius drawn to tangent point (3,6) is VERTICAL.
Since this radius and line M must be perpendicular, line M must be HORIZONTAL.
Since horizontal line M passes through (3,6), it must also pass through (6,6).
SUFFICIENT.

The correct answer is B.