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In the figure above, points P and Q lie on the circle with

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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 10 Dec 2013, 06:34
Bunuel wrote:
zz0vlb wrote:
I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.


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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).


Is it the case of reflection in Y axis ?
I doubt that but still want to clarify..
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 10 Dec 2013, 06:40
ygdrasil24 wrote:
Bunuel wrote:
zz0vlb wrote:
I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.


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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).


Is it the case of reflection in Y axis ?
I doubt that but still want to clarify..


No. \((-\sqrt{3}, 1)\) is not a reflection of \((1, \sqrt{3})\) around the Y-axis. The reflection of \((1, \sqrt{3})\) around the Y-axis is \((-1, \sqrt{3})\).
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 24 Jul 2015, 06:28
Bunuel wrote:
zz0vlb wrote:
I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.


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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).


Hi Bunuel

Cant we do this by applying 45-45-90 getting distance between O and Q as 1/sqroot 3? As OP=OQ (radii)? but with this I get t/s=1/sqroot3. Pls advise
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 24 Jul 2015, 07:10
sinhap07 wrote:
Bunuel wrote:
zz0vlb wrote:
I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.


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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).


Hi Bunuel

Cant we do this by applying 45-45-90 getting distance between O and Q as 1/sqroot 3? As OP=OQ (radii)? but with this I get t/s=1/sqroot3. Pls advise


Let me try to answer this.

\(\angle{POA} = 30\) by following steps:

In triangle POA, OA = \(\sqrt{3}\), AP = 1, thus this triangle is a 30-60-90 (as the sides are in the ratio \(1:\sqrt{3}:2\)) triangle (either remember this or use trigonometry to figure it out!).

Now, per your question, triangle OPQ is isosceles with 45-45-90 triangle and sides in the ratio \(1:1:\sqrt{2}\)

Thus, PQ should be = \(\sqrt{2}\) and not 1/sqroot 3
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 16 May 2016, 13:37
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Hello all, I just got this question in my GMATprep practice test, and came looking here for an explanation afterwards.

I understand the math in the comments above, and why the answer is what it is. What concerns me, is that the image is not drawn to scale.
It did not say the image was not drawn to scale, and this is an official question, so why could I not assume the image was drawn to scale?

(When one has time to look at the question properly it is obvious that it is not drawn to scale - but I have up to now just been assuming that geometry questions are drawn to scale unless clearly indicated that they are not.)
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 17 May 2016, 01:39
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etienneg wrote:
Hello all, I just got this question in my GMATprep practice test, and came looking here for an explanation afterwards.

I understand the math in the comments above, and why the answer is what it is. What concerns me, is that the image is not drawn to scale.
It did not say the image was not drawn to scale, and this is an official question, so why could I not assume the image was drawn to scale?

(When one has time to look at the question properly it is obvious that it is not drawn to scale - but I have up to now just been assuming that geometry questions are drawn to scale unless clearly indicated that they are not.)


You cannot solve the questions by assuming that the diagram is drawn to scale. Two angles which look equal may not actually be equal. You can just assume the basics - straight lines that look straight are straight; points are in the order in which they are drawn. But don't take calls based on relative length of lines, relative measure of angles according to the diagram drawn etc.
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 17 May 2016, 02:12
etienneg wrote:
Hello all, I just got this question in my GMATprep practice test, and came looking here for an explanation afterwards.

I understand the math in the comments above, and why the answer is what it is. What concerns me, is that the image is not drawn to scale.
It did not say the image was not drawn to scale, and this is an official question, so why could I not assume the image was drawn to scale?

(When one has time to look at the question properly it is obvious that it is not drawn to scale - but I have up to now just been assuming that geometry questions are drawn to scale unless clearly indicated that they are not.)


OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 25 Mar 2018, 08:00
can you pls explain the answer to this question in detail.
thankyou!

Bunuel wrote:
zz0vlb wrote:
I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.


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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 25 Mar 2018, 08:27
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pranavpal wrote:
can you pls explain the answer to this question in detail.
thankyou!

Bunuel wrote:
zz0vlb wrote:
I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.


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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\);
Point P in II quadrant \((-\sqrt{3}, 1)\);
Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP);
Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).


Hi pranavpal,

Many people have already solved the Q in prev posts, but I will attempt it as you pinged on main chat :-) Hope I can help.

Let PO make an angle of x (angle POA) with the negative x axis.. this angle comes out to 30 degrees using the tangent rule... ( i.e the slope of line PO is 1/sq root 3)

This angle is complementary to the angle made by QO with the positive X axis ... hence the angle QOB is 90 - 30 = 60 degrees.

In the two traingles POA and QOB... only the hypotenuse is common and we can call this to be r (as it is also the radius of the circle)

Applying the cosine rule on both right angled triangles..

1) \(\sqrt{3}/r = \sqrt{3}/2\) ... applying the cosine rule on POB triangle.

This gives us r = 2.

2) \(s / r = 1/2\) ... cosine rule on right angled traingle QOA. ( we know r = 2 from above)

Hence s = 1.

Option (B).

To see a video about cosine rule and tangent rule these can be very helpful to solve advanced geometry questions-> https://www.youtube.com/watch?v=bDPRWJdVzfs

Hope it makes sense.

Best,
Gladi
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 31 Mar 2018, 18:33
I think I understand how to solve the problem now, but I am having trouble understanding one assumption that people are making in many of the solutions: that O is at the origin. When I tried to solve this problem in the practice test I got to the point where I knew the radius was 2 and that line QO had a slope that was the negative reciprocal of line PO (since they were perpendicular bisectors), but I couldn't solve for slope m of line QO because I was stuck with 1=-sqrt(3)*m+b.

Can we assume that O is at the origin even though it isn't stated in the question, just because it looks like it is? Why can we assume that and not that the y-axis is equidistant from points P and Q (the diagram shows the y-axis passing directly in the middle of the 90 degree angle shown)?
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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 01 Apr 2018, 02:31
ktjorge wrote:
I think I understand how to solve the problem now, but I am having trouble understanding one assumption that people are making in many of the solutions: that O is at the origin. When I tried to solve this problem in the practice test I got to the point where I knew the radius was 2 and that line QO had a slope that was the negative reciprocal of line PO (since they were perpendicular bisectors), but I couldn't solve for slope m of line QO because I was stuck with 1=-sqrt(3)*m+b.

Can we assume that O is at the origin even though it isn't stated in the question, just because it looks like it is? Why can we assume that and not that the y-axis is equidistant from points P and Q (the diagram shows the y-axis passing directly in the middle of the 90 degree angle shown)?


O is the origin because it's on the intersection of x and y axis. Also, if we did not know that, we would not be able to solve the question and since it's a PS questions, we should be able to.

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the figure above, points P and Q lie on the circle with [#permalink]

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New post 19 Apr 2018, 14:39
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christoph wrote:
Image

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


A. \(\frac{1}{2}\)

B. \(1\)

C. \(\sqrt{2}\)

D. \(\sqrt{3}\)

E. \(\frac{\sqrt{2}}{2}\)


[Reveal] Spoiler:
Attachment:
image.JPG


Here's one approach:
Image

So, s = 1

Answer: B

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Brent
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Re: In the figure above, points P and Q lie on the circle with   [#permalink] 19 Apr 2018, 14:39

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