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In the figure above, points P [#permalink]
 13 Nov 2008, 03:35
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Re: GMATPREP- semicircle [#permalink]
13 Nov 2008, 08:01
good one really...
at 1st sight, s looks as sqrt3
radius=2
now, distance between P and Q=2sqrt2
now (s+sqrt3)^2 + (t-1)^2 =8
to solve this equation i need sqrt3 value for T, hence t=sqrt3
Hence s=1.
(if u look at the equation closely, it'll be clear....)
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Re: GMATPREP- semicircle [#permalink]
13 Nov 2008, 12:06
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prasun84 wrote: good one really...
at 1st sight, s looks as sqrt3
radius=2
now, distance between P and Q=2sqrt2
now (s+sqrt3)^2 + (t-1)^2 =8
to solve this equation i need sqrt3 value for T, hence t=sqrt3
Hence s=1.
(if u look at the equation closely, it'll be clear....) it s an interesting method we will have to rely on hit and trial to get the answer My approach Starting from the -ve X axix the order of angles formed will be 30,60,30,60 hence applying tan60 in the triangle created in the first quadrant will have sides hypotenuse= 2 base=1 (which is s) perpendicular =root 3(which is t) hence s is 1
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Re: GMATPREP- semicircle [#permalink]
13 Nov 2008, 20:00
calculate radius of the circle
radius^2= (sqrt(3))^2 + 1^2
radius = 2 (cant be -ve)
the equation of line passing through point P is,
y = -1/sqrt(3)x [ slope = (1-0)/(-sqrt(3) - 0) and y intercept of the line is 0)
The line passing through point Q is perpendicular to the above line
hence its equation is
y = sqrt(3)x
i.r t = sqrt(3)*s
Now OQ being radius can be expressed as
OQ^2 = s^2 + t^2
2^2 = s^2 + (sqrt(3)*s)^2
4 = S^2 * 4
S^2 = 1
S= 1 (being in Ist quadrant)
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Re: GMATPREP- semicircle [#permalink]
13 Nov 2008, 21:42
Thats a very intelligent ans. but shldnt slope of OP be -1/sqrt(3)? (slope=difference in y/difference in x) alpha_plus_gamma wrote: calculate radius of the circle
radius^2= (sqrt(3))^2 + 1^2
radius = 2 (cant be -ve)
the equation of line passing through point P is,
y = -sqrt(3)x [ slope = (-sqrt(3) - 0) / (1-0) and y intercept of the line is 0)
The line passing through point Q is perpendicular to the above line
hence its equation is
y = sqrt(3)x
i.r t = sqrt(3)*s
Now OQ being radius can be expressed as
OQ^2 = s^2 + t^2
2^2 = s^2 + (sqrt(3)*s)^2
4 = S^2 * 4
S^2 = 1
S= 1 (being in Ist quadrant)
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Re: GMATPREP- semicircle [#permalink]
13 Nov 2008, 21:48
Wow ! wht a shortcut. Applying angle formula never occured to me. +1 from me hibloom wrote: prasun84 wrote: good one really...
at 1st sight, s looks as sqrt3
radius=2
now, distance between P and Q=2sqrt2
now (s+sqrt3)^2 + (t-1)^2 =8
to solve this equation i need sqrt3 value for T, hence t=sqrt3
Hence s=1.
(if u look at the equation closely, it'll be clear....) it s an interesting method we will have to rely on hit and trial to get the answer My approach Starting from the -ve X axix the order of angles formed will be 30,60,30,60 hence applying tan60 in the triangle created in the first quadrant will have sides hypotenuse= 2 base=1 (which is s) perpendicular =root 3(which is t) hence s is 1 |
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Re: GMATPREP- semicircle [#permalink]
13 Nov 2008, 21:55
ritula wrote: Thats a very intelligent ans. but shldnt slope of OP be -1/sqrt(3)? (slope=difference in y/difference in x)
Yes you are correct. I have edited my post. thanks
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Re: GMATPREP- semicircle [#permalink]
14 Nov 2008, 12:28
There's a much faster way to do this problem. To find the coordinates of q, all you have to do is switch the x- and y- values of the coordinates of P, then multiply the new y-value (t) by -1.
To understand why, imagine the full circle. Draw any two perpendicular lines through the center. They will intersect the circle at (a, b), (b, -a), (-a, -b), and (-b, a).
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Re: GMATPREP- semicircle [#permalink]
14 Nov 2008, 12:45
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Re: GMATPREP- semicircle
[#permalink]
14 Nov 2008, 12:45
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