Butterfly Theorem
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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
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Link to a good proof :
http://agutie.homestead.com/FiLEs/GeometryButterfly.html
