Butterfly Theorem

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Let $D$ be the midpoint of chord $BC$ of a circle, through which two other chords $EH$ and $FG$ are drawn. $EG$ and $HF$ intersect chord $BC$ at $I$ and $J$, respectively. The Butterfly Theorem states that $D$ is the midpoint of $IJ$.

<geogebra>ac0eaced14d78b0f4ff370ae453962b4db309b5f</geogebra> 

Proof

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See also

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