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23 Jun 2021, 02:00
Kudos
Bookmarks
C
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Difficulty:
35%
(medium)
Question Stats:
66% (01:48) correct
34%
(01:43)
wrong
based on 35
sessions
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Not Attempted Yet
P is a circle with radius r. If AB is a chord in circle P, is AB<6?
(1) r=5
(2) The height from the center of P to AB is smaller than 4.
(1) r=5
(2) The height from the center of P to AB is smaller than 4.
23 Jun 2021, 06:07
Kudos
Bookmarks
Bunuel
Statement 1:
With a radius of 5, the chord can be at least 0 and at most 10 so we don't know if AB is less than 6. Insufficient.
Statement 2:
Without knowing radius this is insufficient.
Combined:
If we let the chord be exactly 6, we can draw the shortest distance from the center to the chord and create a 5 - 4 - 3 triangle, where the mentioned height in statement 2 is exactly 4. Then if we decrease the height, we can see the chord will get longer so the half of the chord is at least 3, and the chord AB in this case would be at least 6. Sufficient.
Ans: C
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