- El 19/01/2013 17:33, Vladimir Dubrovsky escribió:
> Dear Antreas,

The perspector seems to depend only on the two tangents circles to (Ka),

>

> the perspector is called the Eppstein point (one of the two possible) of

> the triange formed by the centers of the three initial circles. See, for

> example, Eppstein, David. “Tangent Spheres and Triangle Centers.” The

> American Mathematical Monthly 108 (2001), pp. 63-66.

>

>

(Kb) and (K,c), an is aligned with its centres, as also the perspector

defined similarly by

(Ka), (Kb) and (K,c) and the inner tangent circle:

http://www.xente.mundo-r.com/ilarrosa/GeoGebra/Malfatti_like_problem.html

>> **

--

>>

>>

>> The perspecivity problem is independent from the triangle!

>>

>> Let (Ka), (Kb), (Kc) be three mutually tangent circles (externally)

>> : (Kb), (Kc) are tangent at A* and (Kc), (Ka) at B* and (Ka), (Kb)

>> at C*. The circle tangent internally to three circles touches (Ka)

>> at A', (Kb) at B', and (Kc) at C'.

>>

>> The lines A'A*, B'B*, C'C* are concurrent (??)

>>

>> Probably it is a well-known problem !!!

>>

>> APH

>>

>>

>> --- In Hyacinthos@yahoogroups.com, "Antreas" wrote:

>>>

>>>

>>> --- In Hyacinthos@yahoogroups.com, "Antreas" wrote:

>>>> Let ABC be a triangle. To draw three circles, each of which

>>>> is tangent to the other two and to one side of ABC and to

>>>> the circumcircle of ABC.

>>>> Note: We can replace circumcircle with an other circle

>>>> (NPC for example)

>>>>

>>>> Figure here

>>>> http://anthrakitis.blogspot.gr/2013/01/a-malfatti-like-problem.html

>>>>

>>>> APH

>>>

>>> Perspective Triangles.

>>>

>>> Let (Ka), (Kb), (Kc) be the three circles.

>>>

>>> (Ka) is tangent to the circumcircle at A', to the BC at A" and to the

>> other two circles (Kb), (Kc) at C*, B*, resp.

>>> (Kb) is tangent to the circumcircle at B', to the CA at B" and to the

>> other two circles (Kc), (Ka) at A*, C*, resp.

>>> (Kc) is tangent to the circumcircle at C', to the AB at C" and to the

>> other two circles (Ka), (Kb) at B*, A*, resp.

>>> The triangles A'B'C', A*B*C* are perspective (??)

>>>

>>> APH

Best regards,

Ignacio Larrosa Cañestro

A Coruña (España)

ilarrosa@...

http://www.xente.mundo-r.com/ilarrosa/GeoGebra/ - Dear David

Thanks!

In my configuration Eppstein point is wrt KaKbKc. The question now

is which are the h. coordinates of the point wrt ABC.

aph

ps

Eppstein points

http://mathworld.wolfram.com/FirstEppsteinPoint.html

http://mathworld.wolfram.com/SecondEppsteinPoint.html

--- In Hyacinthos@yahoogroups.com, Vladimir Dubrovsky wrote:

>

> Dear Antreas,

>

> the perspector is called the Eppstein point (one of the two possible) of

> the triange formed by the centers of the three initial circles. See, for

> example, Eppstein, David. âTangent Spheres and Triangle Centers.â The

> American Mathematical Monthly 108 (2001), pp. 63-66.

>

> Best,

> Vladimir

>

>

> 2013/1/19 Antreas

>

> > **

> >

> >

> > The perspecivity problem is independent from the triangle!

> >

> > Let (Ka), (Kb), (Kc) be three mutually tangent circles (externally)

> > : (Kb), (Kc) are tangent at A* and (Kc), (Ka) at B* and (Ka), (Kb)

> > at C*. The circle tangent internally to three circles touches (Ka)

> > at A', (Kb) at B', and (Kc) at C'.

> >

> > The lines A'A*, B'B*, C'C* are concurrent (??)

> >

> > Probably it is a well-known problem !!!

> >

> > APH

> >

> >

> > --- In Hyacinthos@yahoogroups.com, "Antreas" wrote:

> > >

> > >

> > >

> > > --- In Hyacinthos@yahoogroups.com, "Antreas" wrote:

> > > >

> > > > Let ABC be a triangle. To draw three circles, each of which

> > > > is tangent to the other two and to one side of ABC and to

> > > > the circumcircle of ABC.

> > > > Note: We can replace circumcircle with an other circle

> > > > (NPC for example)

> > > >

> > > > Figure here

> > > > http://anthrakitis.blogspot.gr/2013/01/a-malfatti-like-problem.html

> > > >

> > > > APH

> > >

> > >

> > > Perspective Triangles.

> > >

> > > Let (Ka), (Kb), (Kc) be the three circles.

> > >

> > > (Ka) is tangent to the circumcircle at A', to the BC at A" and to the

> > other two circles (Kb), (Kc) at C*, B*, resp.

> > >

> > > (Kb) is tangent to the circumcircle at B', to the CA at B" and to the

> > other two circles (Kc), (Ka) at A*, C*, resp.

> > >

> > > (Kc) is tangent to the circumcircle at C', to the AB at C" and to the

> > other two circles (Ka), (Kb) at B*, A*, resp.

> > >

> > > The triangles A'B'C', A*B*C* are perspective (??)

> > >

> > > APH