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# Coordinate Geometry Question

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Coordinate Geometry Question [#permalink]  30 Mar 2010, 13:57
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75% (01:54) correct 25% (00:00) wrong based on 4 sessions
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In the Figure, point P and Q lie on the Circle with center O. What is the value of S?

a) 1/2

b) 1

c) sqrt (2)

d) sqrt (3)

e) sqrt (2) / 2

Stumped with the solution to this question. Could someone explain?
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Re: Coordinate Geometry Question [#permalink]  30 Mar 2010, 14:03
both p and q lie on the circle so the PO = QO
PO^2 = QO^2
1+3 = s^2 + t^2
s^2 + t^2 = 4 -- I
PO and QO are perpendicular to each other, so the product of slopes if -1

t/s * 1/-3^1/2 = -1
t = s * 3^1/2 -- II

substituting II in I, we get s = 1

B

Last edited by chix475ntu on 30 Mar 2010, 18:25, edited 1 time in total.
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Re: Coordinate Geometry Question [#permalink]  30 Mar 2010, 18:10
Thank you for the quick response.
[strike]Just to clarify the slopes of PO (absolute value) and QO (absolute value) are not going to be the same when the inside angle is 90? I guess what I'm saying is If we mirrored line PO in to quadrant I and called it XO, the angle of POX would not be 90 degrees, correct?[/strike] Remembered negative reciprocals.

Last edited by gparmar16 on 30 Mar 2010, 18:38, edited 2 times in total.
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Re: Coordinate Geometry Question [#permalink]  30 Mar 2010, 18:27
gparmar16 wrote:
Thank you for the quick response. The solution makes perfect sense to me. For my future reference what allows one to assume point P and Q are perpendicular and hence their respective slopes are equal in this case?

Its given in the figure that the lines are perpendicular. and slopes are not equal but product of slopes is -1.
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Re: Coordinate Geometry Question [#permalink]  30 Mar 2010, 18:29
Great, thank you very much.
Re: Coordinate Geometry Question   [#permalink] 30 Mar 2010, 18:29
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