## Extra de triangulos cabri, In memoriam of Juan Bosco Rom ero Márquez

Expand Messages
• Dear friends of Hyacinthos: The great geometer Spanish Juan Bosco Romero Marquez has died. I dedicate of problem of AMM of 1960,  I deeply regret, was a
Message 1 of 37 , Jan 21, 2013
Dear friends of Hyacinthos:
The great geometer Spanish Juan Bosco Romero Marquez has died.
I dedicate of problem of AMM of 1960,
I deeply regret, was a friend.

Ricardo
http://personal.us.es/rbarroso/trianguloscabri/

[Non-text portions of this message have been removed]
• It is Another Seven Circles Theorem ! The Seven Circles Theorem states: Let a,b ,c, a ,b,c be a closed chain of six circles, all toouching a base circle
Message 37 of 37 , Mar 21, 2013
It is Another "Seven Circles Theorem" !

The "Seven Circles Theorem" states:

Let a,b',c, a',b,c' be a closed chain of six circles,
all toouching a base circle w[omega], and suppose that
their points of contact with w are six distinct points
A,B',C,A',B,C' respectively. Then, subject of a certain
extra condition to be discussed below, AA',BB',CC' are concurrent.
(C J A Evelyn, B G Money - Coutts, J A Tyrrell:
The Seven Circles Theorem and other theorems. London 1974, p. 31)

http://en.wikipedia.org/wiki/Seven_circles_theorem
http://mathworld.wolfram.com/SevenCirclesTheorem.html

APH

--- In Hyacinthos@yahoogroups.com, "Angel" <amontes1949@...> wrote:
>
> Dear Antreas
>
> --- In Hyacinthos@yahoogroups.com, "Antreas" wrote:
> >
> > Dear Alex
> >
> > Angel has tested the loci problems and it seems that
> > for all P's the lines are concurrent for the cevian case,
> > and for the pedal case as well except for the points P on the
> > bisectors and on the circumcircle.
> >
> > Hmmmmmmm...... Maybe it is true in general ie for any
> > circle intersecting the sidelines of the triangle!!
> >
>
>
> A check with GeoGebra:
>
>
>
> Let ABC be a triangle and P a point.
>
> Let (Q) be the CEVIAN circle of P and (Qab), (Qac) the circles touching AB,AC and (Q) internally and let (Tab), (Tac) be the points of contact. Similarly we define the points Tbc, Tba and Tca, Tcb.
>
> For all P (except for the points P on the bisectors) the lines TabTac, TbcTba, TcaTcb are concurrent.
>
> http://amontes.webs.ull.es/geogebra/Hyacinthos21421.html
>
> ----------------------
>
> Let (Q) be the PEDAL circle of P and (Qab), (Qac) the circles touching AB,AC and (Q) internally and let (Tab), (Tac) be the points of contact. Similarly we define the points Tbc, Tba and Tca, Tcb.
>
> For all P (except for the points P on the
> bisectors and on the circumcircle) the lines TabTac, TbcTba, TcaTcb are concurrent.
>
> http://amontes.webs.ull.es/geogebra/Hyacinthos21421Pedal.html
>
> ------------------------------------------------
>
> Let (Q) be the circle Intersecting the sidelines of the triangle in D, E and F. (Qab), (Qac) the circles touching AB,AC and (Q) internally and let (Tab), (Tac) be the points of contact. Similarly we define the
> points Tbc, Tba and Tca, Tcb.
>
> The lines TabTac, TbcTba, TcaTcb are concurrent.
>
> http://amontes.webs.ull.es/geogebra/Hyacinthos21428.html
>
> Best regards,
> Angel M.
>
Your message has been successfully submitted and would be delivered to recipients shortly.