Butterfly Theorem

Butterfly Theorem

In a circle draw a chord PQ with mid-point M. Through M draw 2 chords AB, CD. Join AD, BC cut PQ at X, Y resp. (Butterfly M)

1. Prove: M = mid-point of XY

http://gogeometry.com/GeometryButterfly.html

2. If circle changed to ellipse, still true?

Yes. Affine transformation from circle elongated to ellipse, like distorted image through funny mirror => still MX = MY

Butterfly theorem

Butterfly theorem (Pho

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