Dear Wilson

So I chewed on your ideas.

Are you sure of (1)?

That is to say, if ABC is H-logic with A'B'C', then A'B'C' is H'-logic with

ABC.

This is true for the centroid and the orthocenter but with other centers,

that seems to me very strange!

On the other hand, (1) is true not only for G but for every affine point.

In other words, let (u,v,w) be a triple of barycentrics with u + v + w = 1

Let P be the point having (u,v,w) as barycentrics wrt ABC;

I will say that ABC is (u,v,w)-logic with A'B'C' if the lines through A',

B', C' respectively parallel to AP, BP, CP concur.

Then if ABC is (u,v,w)-logic with A'B'C', then A'B'C' is also (u,v,w)-logic

with ABC.

Friendly

François

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