Difference between revisions of "Butterfly Theorem"
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==Proof== | ==Proof== | ||
{{solution}} | {{solution}} | ||
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Link to a good proof : | Link to a good proof : | ||
http://agutie.homestead.com/FiLEs/GeometryButterfly.html | http://agutie.homestead.com/FiLEs/GeometryButterfly.html | ||
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| + | Also another nice proof by Darij Grinberg can be found here: | ||
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| + | http://www.cip.ifi.lmu.de/~grinberg/Butterfly.zip | ||
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==See also== | ==See also== | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
[[Category:Theorems]] | [[Category:Theorems]] | ||
| + | [[Category:midpoint]] | ||
Revision as of 12:50, 11 July 2010
Let 
be the midpoint of chord 
of a circle, through which two other chords 
and 
are drawn. 
and 
intersect chord at 
and 
, respectively. The Butterfly Theorem states that is the midpoint of 
.
<geogebra>ac0eaced14d78b0f4ff370ae453962b4db309b5f</geogebra>
Proof
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Link to a good proof :
http://agutie.homestead.com/FiLEs/GeometryButterfly.html
Also another nice proof by Darij Grinberg can be found here:
http://www.cip.ifi.lmu.de/~grinberg/Butterfly.zip
