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# GMATPrep Question: Half Circle

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GMATPrep Question: Half Circle [#permalink]  10 Nov 2007, 17:21
Hi, if you know how to solve this problem and you can explain your answer. Please let me know. Also, if you know any shortcut method regarding this question, please let me know too.

I have already looked at the following link, but I still do not get it. http://www.gmatclub.com/forum/t22425
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Solution:

Lets say A and B are two points on circle with coordinates (-sqrt3, 1) and (s,t) respectively. Their distance from the center of the circle, origin in this case will be the same, as it is the radius of the circle.

applying the formula to calculat the distance we will have radius of the circle to be 2. so we have s^2 + t^2 = 4... equation 1.

Also we know that these two lines make right angle at origin. By applying pythagoras them, we have (s+sqrt3)^2 + ( t-1)^2) = 8

On solving and using equation 1, we will get t = sqrt3 * S

Now again putting this value in equation 1, we get s = 1

Amardeep
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