Coordinate Geometry question

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Spartacus2000: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sun May 01, 2011 2:31 pm

by Spartacus2000 » Tue Aug 09, 2011 6:16 pm

In the attached figure, points P and Q lie on the circle with center O. what is the value of s?

(1) 1/2
(2) 1
(3) Root 2 (could not find the symbol for root)
(4) Root 3
(5) Root 2/2

Img. is attached - I hope it is displayed

Thanks.[/img]

Just realized this is in the wrong section, sorry about that.

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 09, 2011 6:16 pm

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by Anurag@Gurome » Tue Aug 09, 2011 9:13 pm

Spartacus2000 wrote:

In the attached figure, points P and Q lie on the circle with center O. what is the value of s?

(1) 1/2
(2) 1
(3) Root 2 (could not find the symbol for root)
(4) Root 3
(5) Root 2/2

Img. is attached - I hope it is displayed

Thanks.[/img]

Just realized this is in the wrong section, sorry about that.

Coordinates of point O, the origin are (0, 0)
Angle POQ = 90Âº, so the slope of OP * slope of OQ = -1 (the product of the slopes of two perpendicular lines is -1).
We can find the slope of OP, as we know their coordinates.
Slope of OP = (1- 0)/(-âˆš3 - 0) = -1/âˆš3
So, slope of OQ = âˆš3/1 or (âˆš3 - 0)/(1 - 0), which implies the x-coordinate of point Q is 1 or s = 1.

The correct answer is B.

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Tue Aug 09, 2011 10:38 pm

Here is a step-by-step description solving this question.

https://www.beatthegmat.com/circle-i-can ... tml#393687

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Aug 10, 2011 2:21 am

I posted an illustrated solution here:

https://www.beatthegmat.com/gmatprep-q-x ... tml#394684

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