Two tangent circles

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• Dear Hyacinthists, during resolving another problem, I have found this one... Let ABC be a right triangle at A and O the midpoint of BC. Prove that the circle
Message 1 of 5 , Sep 21, 2010
Dear Hyacinthists,
during resolving another problem, I have found this one...
Let ABC be a right triangle at A and O the midpoint of BC.
Prove that the circle with diameter AO is tangent to the incircle.
Sincerely
Jean-Louis

[Non-text portions of this message have been removed]
• Dear Hyacinthists, sorry for the simplicity of this problem!!!! Sincerely Jean-Louis ... De: Jean-Louis Ayme Objet: [EMHL] Two tangent
Message 2 of 5 , Sep 21, 2010
Dear Hyacinthists,
sorry for the simplicity of this problem!!!!
Sincerely
Jean-Louis

--- En date de : Mer 22.9.10, Jean-Louis Ayme <jeanlouisayme@...> a écrit :

De: Jean-Louis Ayme <jeanlouisayme@...>
Objet: [EMHL] Two tangent circles
À: Hyacinthos@yahoogroups.com
Date: Mercredi 22 septembre 2010, 7h06

Dear Hyacinthists,
during resolving another problem, I have found this one...
Let ABC be a right triangle at A and O the midpoint of BC.
Prove that the circle with diameter AO is tangent to the incircle.
Sincerely
Jean-Louis

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]
• Circles (N;a/4) and (I;r) touch because  r = s - a = (b + c - a) /2; b + c = 2r + a AI = r / cos pi/4 = r sqrt2,  AN = a/4,  angle IAN = pi/4 ~ C,  cos
Message 3 of 5 , Sep 22, 2010
Circles (N;a/4) and (I;r) touch because
r = s - a = (b + c - a) /2; b + c = 2r + a
AI = r / cos pi/4 = r sqrt2,
AN = a/4,
angle IAN = pi/4 ~ C,
cos (IAN) =  (cos C + Sin C) / (sqrt 2)              =  (b + c) / a (sqrt 2)              =  (2r + a) / a (sqrt 2)
I NI I^2 = I AN I^2 + I AI I^2 - 2. I AN I. I AI I. cos (IAN)            = (a/4)^2 + 2r^2 - 2. (a/4). (r sqrt2). (2r + a) / a (sqrt 2)           = (a/4)^2 + 2(r^2) - r(2r + a) / 2           = (a/4)^2 + r^2 - ar / 2           = (r ~ a/4)^2 etc
--- On Wed, 22/9/10, Jean-Louis Ayme <jeanlouisayme@...> wrote:

From: Jean-Louis Ayme <jeanlouisayme@...>
Subject: Re : [EMHL] Two tangent circles
To: Hyacinthos@yahoogroups.com
Date: Wednesday, 22 September, 2010, 10:56 AM

Dear Hyacinthists,

sorry for the simplicity of this problem!!!!

Sincerely

Jean-Louis

--- En date de : Mer 22.9.10, Jean-Louis Ayme <jeanlouisayme@...> a écrit :

De: Jean-Louis Ayme <jeanlouisayme@...>

Objet: [EMHL] Two tangent circles

À: Hyacinthos@yahoogroups.com

Date: Mercredi 22 septembre 2010, 7h06

Dear Hyacinthists,

during resolving another problem, I have found this one...

Let ABC be a right triangle at A and O the midpoint of BC.

Prove that the circle with diameter AO is tangent to the incircle.

Sincerely

Jean-Louis

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]
• The circle with AO s diameter is nine-point-circle of ABC (hence by feuerbach s thm the problem becomes obvious) (This was sent to the problem setter via email
Message 4 of 5 , Sep 23, 2010
The circle with AO s diameter is nine-point-circle of ABC (hence by feuerbach's thm the problem becomes obvious)

(This was sent to the problem setter via email but wasn't uploaded on hyacinthos so I'm posting again)
• Dear Mathlinkers, 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
Message 5 of 5 , Sep 24, 2010
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

--- In Hyacinthos@yahoogroups.com, Jean-Louis Ayme <jeanlouisayme@...> wrote:
>
> Dear Hyacinthists,
> during resolving another problem, I have found this one...
> Let ABC be a right triangle at A and O the midpoint of BC.
> Prove that the circle with diameter AO is tangent to the incircle.
> Sincerely
> Jean-Louis
>
>
>
>
> [Non-text portions of this message have been removed]
>
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