The theorem is a special case of a more general one, valid for conics (see Tangent_Cuts_Envelope.html ). I was searching for an elementary geometric proof, but was unable to find one. There are also interesting analytic relations involved, I would like to know. For example, the determination of the relation f(r

[1] There is a second circle c

[2] The contact points F, G of the two circles c

[3] There is a position for A, for which lines BC and DE become parallel. Then G falls at infinity and c

Poncelet_Proof.html

Quadratic_Transformation.html

Tangent_Cuts_Envelope.html

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