Difference between revisions of "Butterfly Theorem"
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Revision as of 17:31, 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 simple proof uses projective geometry.
First we note that
Therefore,
Since
,
Moreover,
so
as desired.
.
Link to another proof :
http://agutie.homestead.com/FiLEs/GeometryButterfly.html