The Butterfly Theorem states that if a chord of a circle has its midpoint used as the common point for two further chords, and lines are drawn connecting the endpoints of those two further chords across the first chord, then the first chord's midpoint also bisects the segment cut off between those two crossing lines. It is a classical result of Euclidean circle geometry, named for the butterfly-shaped figure its construction produces.
Facts
StatementIf M is the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn, and AD and BC intersect chord PQ at points X and Y respectively, then M is also the midpoint of XY. 1 Classification
Statement Form Connections
Sources
1. Butterfly Theorem (Wikipedia)
Wikimedia Foundationopening paragraph, statement of the theorem
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.
History section, second sentence
Three solutions were published in 1804, and in 1805 Sir William Herschel posed the question again in a letter to Wallace.
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