Difference between revisions of "Butterfly Theorem"
Line 1: | Line 1: | ||
Let <math>D</math> be the [[midpoint]] of [[chord]] <math>BC</math> of a [[circle]], through which two other chords <math>EH</math> and <math>FG</math> are drawn. <math>EG</math> and <math>HF</math> intersect chord <math>BC</math> at <math>I</math> and <math>J</math>, respectively. The '''Butterfly Theorem''' states that <math>D</math> is the midpoint of <math>IJ</math>. | Let <math>D</math> be the [[midpoint]] of [[chord]] <math>BC</math> of a [[circle]], through which two other chords <math>EH</math> and <math>FG</math> are drawn. <math>EG</math> and <math>HF</math> intersect chord <math>BC</math> at <math>I</math> and <math>J</math>, respectively. The '''Butterfly Theorem''' states that <math>D</math> is the midpoint of <math>IJ</math>. | ||
+ | |||
+ | [[File:528px-Butterfly_theorem.svg.png ]] | ||
==Proof== | ==Proof== |
Revision as of 18:16, 31 May 2011
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
.
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