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Topic: Circle Shifting (Read 1022 times) |
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0.999...
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Circle Shifting
« on: Dec 8th, 2010, 5:36pm » |
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Assume that one can perform only sequences constituted by the following operations (on the plane):
- Given points A, B construction of the line that passes through both A and B;
- Given points C, A construction of the circle that has center C and contains A; and
- The ability to determine intersections.
Given the circle centered at A and containing B, how does one construct the circle centered at any point P with the same radius.
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Noke Lieu
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pen... paper... let's go! (and bit of plastic)
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Re: Circle Shifting
« Reply #1 on: Dec 8th, 2010, 6:41pm » |
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are you saying radius AB, or radius > AB?
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a shade of wit and the art of farce.
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0.999...
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Re: Circle Shifting
« Reply #2 on: Dec 9th, 2010, 2:54am » |
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Radius of the same length as AB.
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Grimbal
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Re: Circle Shifting
« Reply #3 on: Dec 9th, 2010, 8:13am » |
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C = circle with center A containing B
D = circle with center A containing P
E = circle with center P containing A
F = intersection(D,E) (any one)
G = intersection(E, C) (any one)
H = circle with center F containing G
I = intersection(D, H) (you have to chose the right one)
answer = circle with center P containing I.
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| « Last Edit: Dec 16th, 2010, 8:33am by Grimbal » |
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0.999...
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Re: Circle Shifting
« Reply #4 on: Dec 9th, 2010, 1:18pm » |
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If I did not err, there is a process that does not require choosing the correct point.
In your solution I think that in a couple of instances you meant D when you wrote F.
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| « Last Edit: Dec 9th, 2010, 1:56pm by 0.999... » |
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Grimbal
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Re: Circle Shifting
« Reply #5 on: Dec 16th, 2010, 8:39am » |
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fixed.
Another method:
D = circle with center A containing P
E = circle with center P containing A
F, F' = intersection(D,E) (2 points)
H = circle with center F containing B
H' = circle with center F' containing B
I = intersection(H,H') (from the 2 intersections, one is B, the other is I)
answer = circle with center P containing I.
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| « Last Edit: Dec 16th, 2010, 8:39am by Grimbal » |
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