Re: [EMHL] Another point
- On Tue, 4 Jul 2000 xpolakis@... wrote:
>You are right. I wrote my note in haste, and almost at midnight,
> 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)
after coming from my second job back to the Department at that
I will look at your nice question if time permits.
- Dear Alex
> Let us consider the following simply construction:of
> Two circles with the same radius are inscribed in B and C - angles
> triangle ABC correspondently. That circles extouches each othersin the
> point A1.point with
> 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
> trilinears 1/1+sinA,...,... (or 1/(sin(A/2+pi/4))^2,...,...)points in
> It's hard to believe, but I can't find that point among first 300
> ETC.Your point is in ETC as Paasche Point = X(1123) with the same
> May be it is among others?
> Is that point and construction well known?