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GMAT_700
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GMATPrep: Please Help 13 Nov 2007, 15:52
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Hi, if you know how to solve this problem and you can explain your answer. Please let me know. I post this question before, but I did not get the answer.



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singh_amit19
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GMATPrep: Please Help 14 Nov 2007, 10:55
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Please refer to the attached figure:

angle POR = 30 degrees
so angles QOU = 60 degrees so s = 1

I hope this will help :-D
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gmatperp_question_soln.GIF
gmatperp_question_soln.GIF [ 2.38 KiB | Viewed 1174 times ]

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GMATPrep: Please Help 14 Nov 2007, 13:26
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the way i looked at it was:

we know point P and Q are away from O at a distance equal to the radius of the circle.

To find the radius, use the distance formula with point P. I get 4.

Therefore, distance from O to S must be 4 as well. That intuitively gives me coordinates of S = (root 3, 1)
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Amardeep Sharma
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GMATPrep: Please Help 14 Nov 2007, 18:10
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using the formula of calculating the distance between two points we have distance between point P and the origin (center of the circle) = 2 = distance between point S and the origin.

From this we have the equation s^2 + t^2 = 4 (equation of the circle with the center at origin)

Now draw line PS. Using the pythagoras thereom we have:

PS ^2 = 4 + 4 or (sqrt3-s)^2 + (1-t)^2 = 8

or 4 + s^2 + t^2 -2sqrt3s- 2t= 8 (but s^2 + t^2 =4)

so we have t = -sqrt3 *s

putting the value of t in the equation s^2 + t^2 = 4 we get s = 1

Hence answer is s= 1

Amar



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