Soddy circles revisited

jtico shared this question 7 years ago
Answered

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, jtico5a51aae625eab7033db6dedf35e51fae

Files: sd.png

Comments (4)

photo
1

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:

photo
1

Thanks :)


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


jtico.

photo
1

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

photo
1

Good evening.

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

jtico

© 2019 International GeoGebra Institute