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
Is the radius of circle P longer than 2
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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.
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.
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