## Re: Euler Lines (O)

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• ... The homothetic center is the infinite point (b^2-c^2:c^2-a^2:a^2-b^2) Francisco Javier.
Message 1 of 7 , Oct 4, 2008
> The triangles bounded by the lines
> (Lab, Lbc, Lca) and (Lac, Lba, Lcb)
> are homothetic.
>
> Homothetic center?
>
> APH

The homothetic center is the infinite point

(b^2-c^2:c^2-a^2:a^2-b^2)

Francisco Javier.
• ... Let 1,2,3,4,5,..., 2n (n 2) be 2n lines no three passing through a point. Assume that each one line in the set is parallel to only one line in the set.
Message 2 of 7 , Oct 4, 2008
--- In Hyacinthos@yahoogroups.com, "xpolakis" <xpolakis@...> wrote:

> Let 1,2,3,4,5,6 be six lines.
>
> Let 1 // 2 not // 3 // 4 not // 5 // 6 not // 1
>
> How many homethic triangles are there with no common vertex?

Let 1,2,3,4,5,..., 2n (n > 2) be 2n lines no three passing through a
point.

Assume that each one line in the set is parallel to only one line
in the set. ( n dyads of parallel lines)

How many dyads of triangles are formed having no vertex in common?
And how many homothetic dyads of triangles?

APH
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