Butterfly theorem

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For the "butterfly lemma" of group theory, see Zassenhaus lemma.

The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:

Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY.

[edit] External links

• Butterfly theorem, animated proof by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"]
• The Butterfly Theorem at cut-the-knot
• A Better Butterfly Theorem at cut-the-knot
• Proof of Butterfly Theorem at PlanetMath