Generalization of Butterfly's Theorem

Miguel Ochoa Sanchez
28 February, 2017

General Butterfly in Pictures

Part 1

Using Hiroshi Haruki's Lemma

General Butterfly in Pictures, proof, part 1

Part 2

General Butterfly in Pictures, proof, part 2

General Butterfly in Pictures, proof, part 3

Remark

Assuming $a=b,\,$ the main result becomes $(a+z)(y+x)=(b+y)(z+x)\,$ which reduces to $(a-x)(y-z)=0,\,$ and, since $a\ne x,\,$ $y=z,\,$ proving the Butterfly theorem.

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