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A question (and its solution) on an inscribed triangle (TPR)

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Status: Labor Omnia Vincit
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Schools: S3 Asia MBA (Fudan University, Korea University, National University of Singapore)
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A question (and its solution) on an inscribed triangle (TPR) [#permalink]

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New post 02 Sep 2010, 04:01
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

33% (00:00) correct 67% (00:00) wrong based on 3 sessions

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Shouldn't the correct answer to the question in the attached PDF be option D?
[Reveal] Spoiler: OA

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Last edited by rishabhsingla on 05 Oct 2010, 10:56, edited 1 time in total.

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Re: A question (and its solution) on an inscribed triangle (TPR) [#permalink]

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New post 02 Sep 2010, 05:02
Triangle QSR is inscribed in a semi-cirlce is QSR a right triangle?

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

(1) QR is a diameter of the circle --> according to the above property QSR must be a right triangle. Sufficient.

(2) Length QS equals 3 and length QR equals to 5 --> it's not necessary QSR to be 3-4-5 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semi-circle so that SR would be the largest side and QSR would be obtuse-angled triangle. Not sufficient. (Would help if you just try to draw it).

Answer: A.
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Status: Labor Omnia Vincit
Joined: 16 Aug 2010
Posts: 75

Kudos [?]: 3 [0], given: 0

Schools: S3 Asia MBA (Fudan University, Korea University, National University of Singapore)
WE 1: Market Research
WE 2: Consulting
WE 3: Iron & Steel Retail/Trading
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Re: A question (and its solution) on an inscribed triangle (TPR) [#permalink]

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New post 08 Sep 2010, 10:10
Yup now I realize where I was stuck. I was (sub-consciously) assuming that a triangle inscribed in a semi-circle *must* have one of its sides as the diameter of this semi-circle, automatically implying that it's a right triangle.

Thanks folks!

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Re: A question (and its solution) on an inscribed triangle (TPR)   [#permalink] 08 Sep 2010, 10:10
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A question (and its solution) on an inscribed triangle (TPR)

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