Dear friends Hyacinthos: in http://personal.us.es/rbarroso/trianguloscabri/ you can see 628 and 629 issues of the journal Research TRIANGULOSCABRI that the...
Hello: The 629 trianguloscabri is: Let ABC be a triangle. Let sa, sb and sc be lines tangent to a circle concentric with the circumcricle at points of...
Dear Randy, this point was finally included in the ETC under X(3613). How can I contact Clark Kimberkling to let him know more properties about X(3613)? Thanks...
Dear Hyacinthists, an article concerning the “Equal incircles theorem†has been put on my website. http://perso.orange.fr/jl.ayme    vol. 20 Sincerely ...
Dear Jean-Louis, incidentally, recently I've been doing problems similar (often, same) to those in your paper and also came up with yours "4. Un quadrilatère...
Dear Hyacinthists, the line X(2)X(32), containing the points X(83), X(251), X(315), X(626), X(754), also passes through the point Q of homogenous barycentric...
20281
Forum Geometricorum
ForumGeom@...
Nov 4, 2011 7:04 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2011volume11/FG201123index.html The editors Forum...
Dear Friends, Let OH be the circumscribed orthogonal hyperbola of reference triangle ABC through random point P. Let Ce be the Center of OH. Proof that Ce is...
Dear Francois, The orthogonal hyperbola I mean is defined by A,B,C,H,P. H = Orthocenter, P = random point unequal A,B,C,H. Now the Center of this Orthogonal...
Dear Alexey and triangle geometers, Alexey has discovered that: Let the incircle of triangle ABC touche its sides in A', B', C'; I and G are the incenter and...
Dear all, I don't think this helps a lot, but I discovered a slightly related conjecture to Chris' problem: consider rectangular hyperbola F that passes...
Dear Chris and Francois [Chris] ... In "Applicationss d'analyse et de géométrie qui ont servi en 1822 de principal fondament au traite des proprietes...
Dear Jean-Pierre, Thanks for the very nice proof and reference. I noticed earlier that Poncelet and Brianchon did some remarkable findings. Probably their time...
Dear Jean-Pierre Is this just the theorem of Faure in case of the rectangular hyperbola? Friendly François ... [Non-text portions of this message have been...
DearJean-Pierre I think we have the following projective theorem: The cevian triangle UVW of P wrt ABC is self polar wrt every conic through the four points A,...
Now if Gamma is a given rectangular hyperbola thru A, B, C and P a moving point on it and let UVW be the P-cevian triangle wrt ABC. The UVW-circumcircle is on...
Dear Francois ... Yes (the orthoptic circle of a rectangular hyperbola is reduced to the center) But, the Faure's theorem is about 1864 and Poncelet discovered...
20295
Alexey Zaslavsky
zasl@...
Nov 8, 2011 6:50 am
Dear Chris, Jean-Pierre and Francois! ... Synthetic proof of this theorem is in our book "Geometry of conics", AMS, 2007. Sincerely...
20296
Alexey Zaslavsky
zasl@...
Nov 8, 2011 6:59 am
Dear Sung Hyun! Me result is the generalization of Thebault theorem and can be reduced to it by projective map. But I don't know can it be used for the proof...
Dear Chris and Francois Just a remark : if ABC is selfpolar wrt a rectangular hyperbola, the hyperbola is member of the pencil of conics going through the...
Dear Chris ... It is exactly the same thing. I mean that A triangle UVW is the cevian triangle of a point of a conic wrt three other ones if and only if UVW is...
Dear Jean-Pierre and Francois, I am not so familiar with poles and polars. I just know the definitions and some theorems. Interesting enough for me to study. ...
Dear Chris ... See my previous message ... Theorem of Faure : If a triangle is selfpolar wrt a conic, its circumcircle is orthogonal to the Monge (or...
Dear Sung Hyun, I noticed something about the property you mention in the rectangular circumhyperbolas: Consider rectangular hyperbola (F) that passes through...
