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The center of a circleby pixel01
Tags: circle 
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#1
Feb1907, 01:30 AM

P: 691

Hi everybody,
I ve got a question : is it possible to identify the center of a given cirle with only a compass? Thanks for reading 


#2
Feb1907, 03:51 AM

P: 406

Pick a point A on the circle. Draw a circle with center A and diameter less than that of the given circle. Mark off the two points B and C where this new circle intersects the given one. Join B and C with the line BC. Bisect BC. The midpoint is D. Draw a straight line through A and D and extend it until it meets the given circle again at E. AE is a diameter. Repeat this process for a second point on the given circle. Where the two diameters meet is the center. 


#3
Feb1907, 04:51 AM

P: 691

Thank you for answering.
But the problem is without a ruler !!! It seems impossible. I have tried many times but failed. 


#4
Feb2007, 02:24 AM

P: 685

The center of a circle
It works without a ruler, though only for a circle that's on a sheet of paper.
Instead of using a ruler fold the paper to make a line visible. 


#5
Feb2007, 02:56 AM

P: 691




#6
Feb2007, 03:56 AM

P: 25



#7
Feb2007, 05:30 AM

P: 691

It's great !. Thank you Jeroen.
Anyway, how can we prove that friends? 


#8
Feb2107, 04:05 AM

P: 25

The method works by drawing a circle, picking two points on it, then draw a series of circles based on where the existing circles.
The final answer is the intersection of the last two circles. All you need to do is write a big formula containing all these circles and resulting in the coordinates of the final intersection and then prove that "the_big_function(center_of_circle, radius_of_circle, point_1_on_circle, point_2_on_circle) = center_of_circle" is true for any input. This would be a start:



#9
Feb2107, 06:35 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,565

I may be wrong but I seem to remember a theorem that any construction that could be done with compasses and straight edge could be done with compasses alone. Of course "drawing a line" has to be interpreted as constructing two points on the line.
Check: http://thesaurus.maths.org/mmkb/entr...ryById&id=4066 


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