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

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

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New post 14 Sep 2018, 01:02
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57% (01:15) correct 43% (01:33) wrong based on 86 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
image003.jpg [ 3.79 KiB | Viewed 618 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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New post 14 Sep 2018, 07:02
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Bunuel wrote:
Image
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

Answer: option A
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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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New post 27 Sep 2018, 19:53
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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New post 27 Sep 2018, 19:58
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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.
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Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 420 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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New post 27 Sep 2018, 20:27
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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New post 01 Dec 2018, 05:26
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 &nbs [#permalink] 01 Dec 2018, 05:26
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