In Euclidean geometry, the butterfly theorem is a classical result 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. == Proof == A formal proof of the theorem is as follows: Let the perpendiculars XX′ and XX″ be dropped from the point X on the straight lines AM and DM respectively.
In Euclidean geometry, the butterfly theorem is a classical result 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. == Proof == A formal proof of the theorem is as follows: Let the perpendiculars XX′ and XX″ be dropped from the point X on the straight lines AM and DM respectively.
Source: Wikipedia "Butterfly theorem" · CC BY-SA 4.0
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