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13 Sep 2018, 02:33
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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:
50% (01:39) correct
50%
(01:47)
wrong
based on 130
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What is the length of diameter PR in the circle shown above?
(1) PQ has length of 6.
(2) QR has length of \(\sqrt{12}\)
Attachment:
image001.jpg [ 3.88 KiB | Viewed 3323 times ]
13 Sep 2018, 03:10
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Bunuel
Question: Diameter = a+b = ?
We must know that we see here three right angle triangles and all triangles are similar triangles (Proof attached)
and \(3/a = b/3\)
Statement 1: PQ has length of 6
i.e. \(a = √(6^2-3^2) = 3√3\)
And now \(b = √3\)
SUFFICIENT
Statement 2: QR has length of \(\sqrt{12}\)
Now b can be calculated using pythagorus theorem and then a can be calculated as a*b=9 hence
SUFFICIENT
Answer: option D
Attachments
Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 3194 times ]
01 Dec 2018, 06:25
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https://gmatclub.com/forum/if-arc-pqr-above-is-a-semicircle-what-is-the-length-of-diameter-pr-144057.html
Bunnel and other experts posted great detailed solution for similar problem in the above link.
Hope it helps
Bunnel and other experts posted great detailed solution for similar problem in the above link.
Hope it helps
22 Jun 2020, 06:04
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Hi
Can anyone explain how you find that these triangles are similar? We only know that they each have a right angle but that's not enough?
Thanks !!
Can anyone explain how you find that these triangles are similar? We only know that they each have a right angle but that's not enough?
Thanks !!
