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# What is the length of diameter PR in the circle shown above?

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Math Expert
Joined: 02 Sep 2009
Posts: 53709
What is the length of diameter PR in the circle shown above?  [#permalink]

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13 Sep 2018, 02:33
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:29) correct 39% (01:22) wrong based on 45 sessions

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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 445 times ]

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Re: What is the length of diameter PR in the circle shown above?  [#permalink]

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13 Sep 2018, 03:10
Bunuel wrote:

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:
The attachment image001.jpg is no longer available

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

Attachments

Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 410 times ]

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Re: What is the length of diameter PR in the circle shown above?  [#permalink]

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01 Dec 2018, 06:25
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
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Re: What is the length of diameter PR in the circle shown above?   [#permalink] 01 Dec 2018, 06:25
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