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Butterfly theorem
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{{short description|About the midpoint of a chord of a circle, through which two other chords are drawn}} {{For|the "butterfly lemma" of group theory|Zassenhaus lemma}} [[File:Butterfly theorem.svg|upright=1.0|thumb|{{center|Butterfly theorem}}]] The '''butterfly theorem''' is a classical result in [[Euclidean geometry]], which can be stated as follows:<ref name=Johnson>Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publ., 2007 (orig. 1929).</ref>{{rp|p. 78}} Let {{math|''M''}} be the [[midpoint]] of a [[Chord (geometry)|chord]] {{math|''PQ''}} of a [[circle]], through which two other chords {{math|''AB''}} and {{math|''CD''}} are drawn; {{math|''AD''}} and {{math|''BC''}} intersect chord {{math|''PQ''}} at {{math|''X''}} and {{math|''Y''}} correspondingly. Then {{math|''M''}} is the midpoint of {{math|''XY''}}.
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