- 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

late hour.

I will look at your nice question if time permits.

Michael - 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 others

in 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?

definition.

Friendly.

Jean-Pierre