# Soddy circles revisited

Hi all.

This constructions is inspired by the construction given by Raymond in http://www.geogebra.org/for....

Given a triangle ABC draw the hyperbola with focus B and C through the point A. The point D is the intersection of the branch through the point A. With the circles with centres B and C through D, define the point E and F. The circle with center A through E is tangent to the two first circles. To find the centres of the inner and outer Soddy circles, draw, for example the hyperbola through the point B with focus A and C. The intersection G of the branches of the the hyperbolas through the points A and B is the centre of the inner Soddy circle and the intersection K of the branches not through the points A and B is the centre of the outer Soddy circle.

The construction is not new. In fact, the hyperbolas are called the Soddy hyperbolas of the triangle ABC.

Best regards, jtico

Nice work jtico!

Also the points D,E and F are the points of contact of the incircle and the triangle ABC. I happened to rediscover this method of locating the centres of the Soddy circles about a year and a half ago but was disappointed to learn earlier this year that it was not new. :laughing:

Thanks :)

Well, in geometry it's hard to find something that's easy and new :(

jtico.

Bonjour,

J'ai (re) déccouvert la même construction des centres des cercles de Soddy en utilisant les hyperboles !!!

Avez-vous remarqué que les asymptotes des trois hyperboles sont concourantes (il faut évidemment pour chacune choisir la bonne) ??!!

Je cherche, sans succès pour l'instant, à démontrer cette propriété ... ou plus simplement a trouver des infos sur ce pot remarquable du triangle.

A+

Gérard FROGER

Good evening.

I wasn't aware of this strange property about the asymptotes. I have been unable to demonstrate it.

jtico

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