Dear Antreas and Hyacinthists,

I have consider this question when I was working on this subject. I have tried to use the Rabinowitz's result (

http://perso.orange fr/jl.ayme vol. 3) to prove this concurrence but I haven't found a way to prove it synthetically.

Any isea?

Sincerely

Jean-Louis

--- En date de : Sam 25.9.10, Antreas <

anopolis72@...> a écrit :

De: Antreas <

anopolis72@...>

Objet: [EMHL] Re: A circle tangent to the incircle

À:

Hyacinthos@yahoogroups.com
Date: Samedi 25 septembre 2010, 10h21

There are three circles touching the incircle at three points,

say, Ta,Tb,Tc.

A natural question is:

Is the triangle ABC and the triangle TaTbTc perspective?

That is:

Let ABC be a triangle, and A'B'C', A"B"C" the pedal triangles

of H,I, resp. The circle (A,AB"=AC") intersects AA' at A* between

A,A'. Denote A1 := BC /\ IA*. The circle with diameter AA1 touches

the incircle (I) at Ta. Similarly Tb, Tc.

Question:

Are the triangles ABC, TaTbTc perspective?

APH

--- In Hyacinthos@yahoogroups.com, Jean-Louis Ayme <jeanlouisayme@...> wrote:

>

> Dear Hyacinthists,

> an article IN ENGLISH concerning a circle tangent to the incircle has been put on my website

> http://perso.orange.fr/jl.ayme vol. 6 A circle tangent to the incircle

> Sincerely

> Jean-Louis

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