Difference between revisions of "Butterfly Theorem"
God of Math (talk | contribs) (→Proof) |
Amparvardi (talk | contribs) |
||
Line 5: | Line 5: | ||
==Proof== | ==Proof== | ||
{{solution}} | {{solution}} | ||
+ | |||
+ | |||
Link to a good proof : | Link to a good proof : | ||
http://agutie.homestead.com/FiLEs/GeometryButterfly.html | 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 | ||
+ | |||
==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