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09 Apr 2015, 07:20
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:16) correct
41%
(02:24)
wrong
based on 347
sessions
History
Date
Time
Result
Not Attempted Yet
In the diagram above, A is the center of the circle, angle BAD = 90°, and the area of triangle ABD is \(24\sqrt{3}\). What is the area of the circle?
(1) AB = 12
(2) AD = CD
Kudos for a correct solution.
Attachment:
gdrtq_img1.png [ 10.33 KiB | Viewed 11041 times ]
09 Apr 2015, 08:33
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Bunuel
if AB is given we can find AD and hence area of circle . option A is sufficient.
option B : please refer the attached image .
we can find all the sides of ACE as BC=AC=R.
finally will get an expression in Something*\((R^2)\) = \(24 * \sqrt{3}\) Sufficient.
Attachments
gmatclub.jpg [ 17.33 KiB | Viewed 10038 times ]
10 Apr 2015, 00:05
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Bunuel
1) We know that this is right triangle. We know its area and one of the side AB so we can find AD
\(\frac{(AB * AD )}{2}=24 * \sqrt{3}\)
AB = 12
so \(AD = 4\sqrt{3}\)
AD is a radius so we can find area of circle.
Sufficient
2) AD = CD so triangle ADC equalateral and angle ADC = 60 degrees
Ratio of sides in triangle \(ABD = 1:\sqrt{3}:2\)
So \(AB = R\sqrt{3}\) and \(AD = R\)
\(\frac{(R\sqrt{3} * R )}{2}=24 * \sqrt{3}\)
\(R^2\sqrt{3}=48 * \sqrt{3}\)
\(R=4 \sqrt{3}\)
R is a radius so we can find area of circle.
Sufficient
Answer is D
