Are these triangle **centers** in order to be included in ETC? APH ... [Non-text portions of this message have been removed]...
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Francisco Javier
garciacapitan
May 8, 2012 10:51 am
They are, that is, a cyclic permutation of one of the points gives the same point....
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Bernard Gibert
bernardgibert
May 8, 2012 10:58 am
Dear Quim ... these points are real only when ABC is obtuseangle so I expect this is the end of the story... Best regards Bernard [Non-text portions of this...
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Jean-Louis Ayme
jeanlouisayme
May 8, 2012 12:24 pm
Dear Hyacinthists,  My conjecture  1. ABC a triangle, 2. P a point 3. (1a) the circumcircle of the triangle PBC and circularly 4. A’ the second point of...
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Randy Hutson
rhutson2
May 8, 2012 1:45 pm
There are other centers in ETC that are real only for certain triangles, for exampleX(5000) = WALSMITH POINT, which is complex when ABC is obtuse, and the...
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Jean-Louis Ayme
jeanlouisayme
May 8, 2012 1:51 pm
Dear Mathlinkers, I correct the typo of the note  1. ABC a triangle, 2. P a point 3. (1a) the circumcircle of the triangle PBC and circularly 4. A’ the...
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Chandan Banerjee
cbanerjee.2011
May 8, 2012 1:52 pm
So it seems that the two points which are being discussed in this post are anti-complements of the 1st and 2nd Grinberg Intersections. ... -- CHANDAN [Non-text...
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Chandan Banerjee
cbanerjee.2011
May 8, 2012 2:02 pm
I have posted a solution to this problem here:- http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=478701...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201213index.html The editors Forum...
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CESAR
cesar_e_lozada
May 9, 2012 9:48 pm
Barycentrics: u = f(SA, SB, SC) and f(SA, SB, SC) = 1/((SB+SC)*((SB+SC)*(SA^2-SB*SC)+(SB-SC)*(SA*(SB-SC)+`&+-`(2*sqrt(-SA*SB*SC*(SA+SB+SC)))))) There is + -...
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nguyenle2005usa
May 11, 2012 6:40 am
Dear friends, Theorem 28 of Norman Wildberger's paper, "Universal Hyperbolic Geometry III: First steps in Projective Triangle Geometry" which has recently...
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Angel
amontes1949
May 15, 2012 7:14 pm
Dear Hyacinthists, Given a triangle ABC, let I be the incenter, let F be Feuerbach point, and let t be the tangent in F to the incircle. The perpendiculars...
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Ricardo Barroso
ricardobca
May 15, 2012 8:08 pm
Dear Hyacinthists In http://personal.us.es/rbarroso/trianguloscabri/ two probelms.. a locus of Trigueros R. and  Alhazen problem Best regards Ricardo ...
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César Lozada
cesar_e_lozada
May 17, 2012 6:57 pm
Dear Geometers: Doing a pure mathematical-programming exercise, I tried to find triangle centers on circles concentric with circumcircle, i.e., circles passing...
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Barry Wolk
wolkbarry
May 22, 2012 8:09 pm
From: Angel amontes1949@... ... Here is a generalization. Given three lines L1, L2, L3 that meet at P=(p1,p2,p3), find all lines L such that, if L meets...
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Alexey Zaslavsky
zasl@...
May 23, 2012 11:06 am
Dear colleagues! Let a triangle ABC be given. Consider two extremal problems. (1) Find a point X_p minimizing the sum X_pA^p+X_pB^p+X_pC^p (2) Find a points...
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Chandan Banerjee
cbanerjee.2011
May 24, 2012 12:25 pm
Given a circle and a point P inside it, cut the circle into 8 pieces using chords through P such that the angle between any two consecutive chords is 45...
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Francisco Bellot
p28121941
May 24, 2012 1:10 pm
This is the so called pizza theorem, and it is in fact well known. I suggest search first in the net before posting, say with absolute respect to the opinions...
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Chandan Banerjee
cbanerjee.2011
May 24, 2012 2:44 pm
Thank you for your opinion. I am extremely sorry if I offended you or anyone else. I didn't mean any disrespect....
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Chris Van Tienhoven
chris.vantie...
May 25, 2012 7:20 am
... Dear Francisco, I am glad with every contribution or question. Known or unknown, brilliant or diffuse, thought-out or preliminary, researched or not. Ain't...
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Jim
jbuddenh1
May 25, 2012 12:58 pm
I agree with Chris van Tienhoven. Ideas that some people know, others do not. The group is best served by having open discussion. I welcome all ideas posted...
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Nikolaos Dergiades
ndergiades
May 25, 2012 4:35 pm
Dear Alexey!!! Who is the proposer of this wonderful problem? and what is his proof? My proof is the following: The point that minimizes the sum PA^p + PB^p +...
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rhutson2
May 25, 2012 7:22 pm
Dear Hyacinthists: Does anyone have some magic to find any ETC centers that lie on the antiorthic axis of the excentral triangle? The best I can find is that...
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Chris Van Tienhoven
chris.vantie...
May 25, 2012 9:59 pm
Dear Randy, I can't find any in the range X(1) - X(3514). Best regards, Chris van Tienhoven...
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Alexey Zaslavsky
zasl@...
May 28, 2012 6:03 am
Dear Nikos! Who is the proposer of this wonderful problem? and what is his proof? My proof is the same. Problems (1), (2) were formulated by Protasov and...
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Randy Hutson
rhutson2
May 28, 2012 2:00 pm
Thanks Chris. What about the de Longchamps line of the excentral triangle (line at infinity intercept = X(513), or the Gergonne line of the excentral triangle?...
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Chris Van Tienhoven
chris.vantie...
May 28, 2012 5:39 pm
Dear Randy, [RH] ... I found that the de Longchamps line of the excentral triangle passes through (points in the range X(1)-X(3514): X(239) X(514) X(649) ...
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Randy Hutson
rhutson2
May 28, 2012 6:56 pm
Thanks Chris, but I think these points (line X(239)X(514)) lie on the Lemoine axis of the excentral triangle, not the de Longchamps line of e.t. Randy ... ...
