Difference between revisions of "Butterfly Theorem"
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==Related Reading== | ==Related Reading== | ||
http://agutie.homestead.com/FiLEs/GeometryButterfly.html | http://agutie.homestead.com/FiLEs/GeometryButterfly.html | ||
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http://www.mathematik.uni-muenchen.de/~fritsch/butterfly.pdf | http://www.mathematik.uni-muenchen.de/~fritsch/butterfly.pdf | ||
Revision as of 17:34, 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.
.
Related Reading
http://agutie.homestead.com/FiLEs/GeometryButterfly.html
http://www.mathematik.uni-muenchen.de/~fritsch/butterfly.pdf