## Re: [EMHL] Another point

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• ... You are right. I wrote my note in haste, and almost at midnight, after coming from my second job back to the Department at that late hour. I will look at
Message 1 of 15 , Jul 5, 2000
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On Tue, 4 Jul 2000 xpolakis@... wrote:

>
> Note that this problem is different from the mixtilinear incircles problem.
>
> In the mixtilinear in/ex-circles one, we speak about three circles INSCRIBED
> in the triangle's angles and touching in/externally the circumcircle.
> Their centers lie on the lines AIa etc (angle bisectors), but in my problem
> above the centers of the three circles ARE the points Ix (and they are NOT
> inscribed in the angles of the triangle)
>

You are right. I wrote my note in haste, and almost at midnight,
after coming from my second job back to the Department at that
late hour.
I will look at your nice question if time permits.

Michael
• Dear Alex ... of ... in the ... point with ... points in ... Your point is in ETC as Paasche Point = X(1123) with the same definition. Friendly. Jean-Pierre
Message 2 of 15 , May 18, 2003
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Dear Alex
> Let us consider the following simply construction:
> Two circles with the same radius are inscribed in B and C - angles
of
> triangle ABC correspondently. That circles extouches each others
in the
> point A1.
> The points B1 and C1 let us define in the same way.
> So, if I don't mistake, the lines AA1, BB1, CC1 concur in the
point with
> trilinears 1/1+sinA,...,... (or 1/(sin(A/2+pi/4))^2,...,...)
> It's hard to believe, but I can't find that point among first 300
points in
> ETC.
> May be it is among others?
> Is that point and construction well known?

Your point is in ETC as Paasche Point = X(1123) with the same
definition.
Friendly.
Jean-Pierre
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