I have a strange result. Let P be any point on the conic through ABCHI. Then the cevian circle of P goes through the Feuerbach point. Generalizations? -- ...
One generalization: Let P be any point on the rectangular hyperbola ABCHQ. Then the cevian circle of P goes through the center of the hyperbola (on the...
20998
Alexey Zaslavsky
zasl@...
May 2, 2012 5:48 am
Dear Randy and Barry! Yes this is well known. The synthetic proof is in our with Akopjan book "Geometry of conics". Sincerely...
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forumgeom forumgeom
ForumGeom@...
May 2, 2012 12:58 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201212index.html The editors Forum...
Chandan, I haven't looked at the whole proof yet, but one correction I note: replace 'vertex of the hyperbola' with 'center of the hyperbola'. Best regards, ...
Dear friends, Some years ago Paul Yiu posted at Hyacinthos several results about two interesting points, namely the intersections of the De Longchamps line...
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...
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...
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...
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...
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...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201213index.html The editors Forum...
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 + -...
Dear friends, Theorem 28 of Norman Wildberger's paper, "Universal Hyperbolic Geometry III: First steps in Projective Triangle Geometry" which has recently...
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...
Dear Hyacinthists In http://personal.us.es/rbarroso/trianguloscabri/ two probelms.. a locus of Trigueros R. and  Alhazen problem Best regards Ricardo ...
Dear Geometers: Doing a pure mathematical-programming exercise, I tried to find triangle centers on circles concentric with circumcircle, i.e., circles passing...
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...
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...
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...
... 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...
