Is the radius of circle P longer than 2

[BTGmoderatorDC]

Is the radius of circle P longer than 2?

(1) AB, the longest chord in circle P, is at least 5.

(2) The diameter of circle P is longer than 5.

Which is the sufficient statement?

OA D

[ErikaPrepScholar]

Statement 1
If we think about all of the chords we can draw in a circle, we should recognize that the longest chord will be one from a point on the circle straight across to the point opposite it on the other side of the circle - in other words, the longest chord in a circle is the diameter of the circle.

So if the longest chord in circle P is at least 5, the diameter of circle P is at least 5. The radius of a circle is half of the diameter. So if the diameter of circle P is at least 5, the radius is at least 2.5. Sufficient.

Statement 2
This directly tells us that the diameter of circle P is at least 5. Using the same logic from the previous statement, we can determine that the radius of circle P is at least 2.5 Sufficient.