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# If PR is the diameter, what is the length of QP in the circle shown ab

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Math Expert
Joined: 02 Sep 2009
Posts: 55609
If PR is the diameter, what is the length of QP in the circle shown ab  [#permalink]

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14 Sep 2018, 02:02
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:49) correct 42% (02:04) wrong based on 100 sessions

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If PR is the diameter, what is the length of QP in the circle shown above?

(1) b = 2
(2) PQR is a right angle

Attachment:

image003.jpg [ 3.79 KiB | Viewed 798 times ]

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Re: If PR is the diameter, what is the length of QP in the circle shown ab  [#permalink]

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14 Sep 2018, 08:02
1
Bunuel wrote:

If PR is the diameter, what is the length of QP in the circle shown above?

(1) b = 2
(2) PQR is a right angle

Attachment:
image003.jpg

Here we see three right angle triangles and all are similar triangles

Due to similarity ratio, $$1/a = b/1$$

i.e. $$ab = 1$$

Question: Length of QP = ?
To answer this question we only need the either a or b so that we can calculate hypotenuse of right triangle with hypotenuse PQ

Statement 1: b = 2

SUFFICIENT

Statement 2: PQR is a right angle

We already know this hence this is redundant information

NORT SUFFICIENT

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Re: If PR is the diameter, what is the length of QP in the circle shown ab  [#permalink]

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27 Sep 2018, 20:53
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???

Thanks
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Re: If PR is the diameter, what is the length of QP in the circle shown ab  [#permalink]

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27 Sep 2018, 20:58
1
Shank18 wrote:
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???

Thanks

It came using similar triangle property as attached here.
Attachments

File comment: www.GMATinsight.com

Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 588 times ]

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Re: If PR is the diameter, what is the length of QP in the circle shown ab  [#permalink]

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27 Sep 2018, 21:27
GMATinsight wrote:
Shank18 wrote:
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???

Thanks

It came using similar triangle property as attached here.

Thank you so much. This is exactly what I needed
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Re: If PR is the diameter, what is the length of QP in the circle shown ab  [#permalink]

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01 Dec 2018, 06:26
https://gmatclub.com/forum/if-arc-pqr-a ... 44057.html

Bunnel and other experts posted great detailed solution for similar problem in the above link.

Hope it helps
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Re: If PR is the diameter, what is the length of QP in the circle shown ab   [#permalink] 01 Dec 2018, 06:26
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