Art of Problem Solving

Butterfly Theorem: Difference between revisions

No edit summary
Line 9: Line 9:


http://agutie.homestead.com/FiLEs/GeometryButterfly.html
http://agutie.homestead.com/FiLEs/GeometryButterfly.html


==See also==
==See also==
[[Category:Geometry]]
[[Category:Geometry]]
[[Category:Theorems]]
[[Category:Theorems]]

Revision as of 13:58, 25 April 2009

Let $D$ be the midpoint of chord $BC$ of a circle, through which two other chords $EH$ and $FG$ are drawn. $EG$ and $HF$ intersect chord $BC$ at $I$ and $J$, respectively. The Butterfly Theorem states that $D$ is the midpoint of $IJ$.

<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

See also