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# Diagram - Semicircle with point O as center. Y axis is

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Diagram - Semicircle with point O as center. Y axis is [#permalink]  03 May 2006, 18:06
Diagram - Semicircle with point O as center. Y axis is bisecting the semicircle and x axis is the diameter of the circle (passes though point O). Central angle of 90 degrees yields points P (-srt3, 1) and Q (s, t) on the circle.

What is the value of s?

I guessed +srt3 because the diagram looked symetrical about the y axis.

The correct answer that was given is 1.
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Re: GMATPrep - geometry [#permalink]  03 May 2006, 20:42
If I'm not mistaken, if P and Q are 'on' the circle formed by the 90 degrees, then P(-srt3, 1), isn't 1 the radius? Thus, Q should have an x value of 1 as well
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Attaching the diagram. Ignore my poor drawing skills.

I don't see why when P (-sqrt3, 1) the x value of Q (or s) should be 1.
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GF8U2170.jpg [ 44.78 KiB | Viewed 1219 times ]

VP
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The points formed may not be symmetrical. The triangles formed are identical triangles and these are 30:60:90 triangles so the sides are 1:3^(1/2):2 with the radius being 2

Please execuse my drawing, my drawing is pretty elementary but you get the point
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Circle.jpg [ 7.46 KiB | Viewed 1162 times ]

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Actually, I took a different approach. Please let me know if there is any error in my method.

The distance from (sqrt3,1) to the origin would also be the radius of the circle.
Therefore,
length of line OP = srt((-srt(3)-0}^2 + (1-0)^2)]
= srt(3+1) = srt4
= 2
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Actually, I took a different approach. Please let me know if there is any error in my method.

The distance from (sqrt3,1) to the origin would also be the radius of the circle.
Therefore,
length of line OP = srt((-srt(3)-0}^2 + (1-0)^2)]
= srt(3+1) = srt4
= 2

Yes, that's how I knew it was a 30:60:90 triangle
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Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Manager
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I still don't get it. How do you know it is a 30-60-90. Can you please send the complete explanation
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Loner wrote:
I still don't get it. How do you know it is a 30-60-90. Can you please send the complete explanation

a 30-60-90 triangle have sides of x, 2x, and x*3^(1/2), in this case, 1, 2, and 3^(1/2), it is just a rule that you have to remember.

And a 45-45-90 triangle have sides of x, x, x*2^(1/2)
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Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Manager
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Gosh! I was missing a minor point. Thanks a ton buddy!
Intern
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Attaching the diagram. Ignore my poor drawing skills.

I don't see why when P (-sqrt3, 1) the x value of Q (or s) should be 1.
Attachments

GF8U2170.jpg [ 44.78 KiB | Viewed 1184 times ]

Manager
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Where is this problem from?
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You can solve it without knowing about the nature of the ▲.

__2
OP = 3 + 1 = 4
__2
OQ = s**2 + t**2
__2
PQ = (s+√3)**2 + (t-1) **2

Apply the Pythagorean rules and equate the sum of the two sides to the hypotenuse. You would get s = +/-1. Since s is above the x-axis you should have s = 1.
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Thanks,
Zooroopa

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# Diagram - Semicircle with point O as center. Y axis is

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