Proofs:

Note to Angle Sigma:

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Proof 1:  Angle Sigma

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Proof 2: Collinearity of points Pa, Pb, Pc and G

This proof is independent of angle φ = φa = φb = φc (cf. Fig. 08 of the website)

and is therefore also valid for the theorem with  common tangents to the McCay circles!

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Proof 3: After the Affine Transformation the Angle  ε = 45°

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Proof 4: 

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Proof 5: 

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Proof 6:

... that the c-McCay circle is also the G-Apollonius circle of line segment McCbr:

... see proof 3.

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