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In the figure,if POQ is 90deg.then what is the value of t?

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In the figure,if POQ is 90deg.then what is the value of t? [#permalink]

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In the figure,if POQ is 90deg.then what is the value of t?
1. The value of r is -root3
2. The y-coordinate of point P is 1
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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 10:09
Since P and Q are on the circumference of the circle and angle POQ = 90, Pand Q are reflections along Y axis.

from 1) r = -square root(3) so t = square root(3)
from 2) y coordinate is 1. Since radius is not known it is difficult to find the x co ordinate.

1) alone is sufficient but 2) alone is not sufficient. So answer is "A"

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 10:57
The question nowhere states that P & Q are reflections along Y axis.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 11:06
P and Q are on the circumference of the circle.
so OP = OQ
and POQ = 90 degrees. As P and Q are on the same side of X axis,
that implies P and Q are reflections along Y axis.
It is the conclusion we arrived at based on the above conditions.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 11:23
I still didn't get it...:(

Is it not possible that OP makes an angle of 30 degree with Y axis and OQ makes an angle of 60 degress then in such a case POQ is 90 degree but P & Q are not reflections and r will not be equal to t.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 11:33
If P makes 30 and Q makes 60 then P and Q will not be on the circumference of the circle. If P and Q are on the circumference then P, Q make 45 degrees with Y axis.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 11:48
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I am sorry but i don't agree with your point as there can be many points where POQ can be 90 degrees with OP & OQ making angles other than 45degree and still remain on circumference since OP & OQ are radius and they will always be on circumference.

Just try to imagine that you are rotating OP and OQ such that angle between them is 90 and there could be many such points and OP & OQ will still stay on circumference.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 12:30
You are right there are many possible combinations of angles. Thanks for pointing this out. What will be the answer for this question then?

Last edited by Aleehsgonji on 25 Jul 2009, 12:47, edited 1 time in total.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 12:40
I guess it should be C since we know r & s so we can calculate radius and the angle that OP with X & Y axis.So we can then get angle that OQ makes with X & Y axis.NOW OP = OQ and we know the angle that OQ makes with X axis so we can calculate t & u.

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Re: what is the value of t? [#permalink]

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New post 25 Jul 2009, 13:18
it is clear that statement 1 & 2 is not sufficient

on combining both 1&2 => we know the radius of the circle 'x' by distant formula ( we know co ordinate of P (root3 , 1) )

Now think of this as we are at (0,0) => we can draw a circle of radius 'x' got from both eqns => now on the drawn semicircle; we can plot point (root3,1) and hence line from this point to (0,0) => also we can draw perpendicular to his line ending on semicirlcle at Q (t,u) now => if a point Q can be found by construction ; its co-ordinates also can be found out.... hence C

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Re: what is the value of t? [#permalink]

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New post 26 Jul 2009, 08:02
Yes, it is logical that we can find the coordinates of Q.
Can anyone give a calculation on how we can derive the values of coordinates of Q from the given information in 1) and 2) ?

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Re: what is the value of t? [#permalink]

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New post 26 Jul 2009, 08:26
From 1 and 2,
coordinates of P(-squareroot(3), 1)

Angle made by OP with Y axis Tan angle = (x coordinate) / (Y coordinate)
= |-(squareroot 3)/1| = 60
So angle made by Q with Y axis = 90 - 60 = 30
Tan 30 = (x coordinate) / (Y coordinate) = 1/(square root 3)
but as OQ = 2, common factor for the ratio of x and y coordinates of Q is 1.
So Q = (1, square root(3))

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Re: what is the value of t? [#permalink]

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New post 27 Jul 2009, 01:54
Use the similar/equilateral triangles to solve this!

Assuming (p,s as positive numbers)

Line with (-p,s) will be perpendicular to the one with
==> (s,p) in First quadrant
==> (-s,-p) in the third quadrant.
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Re: what is the value of t? [#permalink]

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New post 27 Jul 2009, 01:57
sudeep wrote:
Use the similar/equilateral triangles to solve this!

Assuming (p,s as positive numbers)

Line with (-p,s) will be perpendicular to the one with
==> (s,p) in First quadrant
==> (-s,-p) in the third quadrant.

Did'nt get your explanation. p,s as positive integers? P is a point and s is a coordinate of P !?

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Re: what is the value of t? [#permalink]

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New post 27 Jul 2009, 02:14
Economist wrote:
sudeep wrote:
Use the similar/equilateral triangles to solve this!

Assuming (p,s as positive numbers)

Line with (-p,s) will be perpendicular to the one with
==> (s,p) in First quadrant
==> (-s,-p) in the third quadrant.

Did'nt get your explanation. p,s as positive integers? P is a point and s is a coordinate of P !?


I am saying assume that we have two positive numbers (p and s)
because (-p, s) will then be in the second quadrant in that case.

Further regarding reasoning, draw perpendicular from point P and S on X axis.
The two resulting triangles, one in first quadrant and other in second quadrant will be equivalent.

Reason for equilateral:

First they are similar: you can easily see that in the figure for angles.

Now as one side is also of same length of two triangles (=radius)
==> they are equilateral

the difference ==> y distance will become x distance and vice versa for the coordinates.
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Last edited by sudeep on 28 Jul 2009, 14:45, edited 1 time in total.

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Re: what is the value of t? [#permalink]

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New post 27 Jul 2009, 10:28
If you are tranforming by 90 degree that is a transformation across the quadrant. Whenever you transform in that way an original coordinate (r,s) -> (-s, r)
(If it was a 180 degree transformation, it would have been (r,s)->(-r, -s), i.e. value will negate but not their position). What is the source of the question btw? IS it OG or a third party vendor?

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Re: what is the value of t?   [#permalink] 27 Jul 2009, 10:28
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In the figure,if POQ is 90deg.then what is the value of t?

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