# The Butterfly Theorem

The Butterfly Theorem
Draw a circle, choose any chord PQ, and draw two
further chords AB and CD through its midpoint M.
Now, if AD and BC intersect PQ at X and Y, M will
always be the midpoint of XY.
In Icons of Mathematics (2011), Claudi Alsina and
Roger Nelsen write, “The surprise is the unexpected
symmetry arising from an almost random construction.”
The theorem first appeared in 1815.
credit: Greg Ross
http://www.futilitycloset.com/2014/12/09/the-butterfly-theorem/
commons.wikimedia.org

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