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
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