Butterfly Theorem
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
