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655-705 (Hard)|   Geometry|      
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Bunuel
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If PR is the diameter, what is the length of QP in the circle shown ab 14 Sep 2018, 02:02
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55% (hard)

Question Stats:

59% (01:45) correct 41% (01:47) wrong based on 111 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


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If PR is the diameter, what is the length of QP in the circle shown ab 14 Sep 2018, 08:02
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Bunuel

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


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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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If PR is the diameter, what is the length of QP in the circle shown ab 27 Sep 2018, 20:53
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Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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If PR is the diameter, what is the length of QP in the circle shown ab 27 Sep 2018, 20:58
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Shank18
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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It came using similar triangle property as attached here.
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File comment: www.GMATinsight.com
Geometry 7 Similar Triangle Latest.jpg
Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 3163 times ]

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If PR is the diameter, what is the length of QP in the circle shown ab 27 Sep 2018, 21:27
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Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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It came using similar triangle property as attached here.
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Thank you so much. This is exactly what I needed
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If PR is the diameter, what is the length of QP in the circle shown ab 01 Dec 2018, 06:26
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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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If PR is the diameter, what is the length of QP in the circle shown ab 20 Dec 2023, 07:36
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ShankSouljaBoi
Hi @GAMTinsight How did you get to ab = 1. Can you please explain the similarity ratio used a bit more ???


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You can also approach it algebraically.

\(c^2=\)hypotenuse big triangle
\(d^2=\)hypotenuse small triangle


\( a^2+1= c^2\)
\(b^2+1= d^2\)
Substitution \( c^2+d^2= 〖(a+b)〗^2\)
Expansion of the quadratic \(a^2+1+b^2+1=a^2+2ab+b^2\)
Simplification \(2=2ab -----> 1=ab\)


I hope this helps
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