The points P and Q lie on a circle with centre O. The coordinates of point P are (-√3, 1). The coordinates of point Q are (s,t). It is given that angle POQ = 90 degrees, What is the value of s?
1. ½
2. 1
3.√2
4. √3
5. √2/2
My query
This problem appeared in my GMATPrep (old) Practice Test 02. This problem actually has an image which I am not being able to place here (tech issue??). I solved for the distance OP = 2 units using Pythagorus theorum.
OP = OQ as radii of a circle are equal.
But I do not know how to proceed. Please help.
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- shah-kartik
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- kre
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Re: Points P and Q lie on a circle
The triangle created in QII is a 30/60/90 triangle with the longer side sqrt(3) on the x axis. Therefore that angle's 30, add the 90 degrees given in the question, and the triangle created in QI is also a 30/60/90 but with the 60 degree angle on the x axis (180 degrees - 90 - 30).
because the lengths are the same (radii of circle), the sides are also 1 and sqrt(3) but flipped.
The question graphic is tricky because it seems to reflect over the y-axis, but not in this case.
because the lengths are the same (radii of circle), the sides are also 1 and sqrt(3) but flipped.
The question graphic is tricky because it seems to reflect over the y-axis, but not in this case.
- bineeshnair4u
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Re: Points P and Q lie on a circle
kre Wrote:The triangle created in QII is a 30/60/90 triangle with the longer side sqrt(3) on the x axis. Therefore that angle's 30, add the 90 degrees given in the question, and the triangle created in QI is also a 30/60/90 but with the 60 degree angle on the x axis (180 degrees - 90 - 30).
because the lengths are the same (radii of circle), the sides are also 1 and sqrt(3) but flipped.
The question graphic is tricky because it seems to reflect over the y-axis, but not in this case.
Ken - the angle will not be 30/60/90.. The question mentions that angle POQ is 90 and OP=OQ so its isoceles right traingle, which means angle will be 45/45/90
- bineeshnair4u
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- kre
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Re: Points P and Q lie on a circle
bineeshnair4u, look at the link you posted again. It's absolutely a 30/60/90 triangle (lengths are sqrt(3), 1, 2), hence the answer to the question is 1.
The question stating that OP = OQ confirms the length of the vectors are the same (2 in this case), and because we can add the angles we know that s=1.
Good luck!
The question stating that OP = OQ confirms the length of the vectors are the same (2 in this case), and because we can add the angles we know that s=1.
Good luck!
- RonPurewal
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