Dear Alexey and Jean-Pierre [AM] ... BC ... not on ... measures in the ... constructing ... [JPE] ... the ... signed. ... such ... when ... means ... another...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200515index.html The editors, Forum...
ForumGeom
ForumGeom@...
Aug 3, 2005 7:54 pm
11451
Dear Hyacintheans; Recently, I have been working on the Fuhrmann triangle and I have a generalization to which I give a synthethic proof (I really don't know...
Hello to all from a long absence, As The Triangle Book is taking a long time to write, I will begin posting some pictures of topics in the book on my web site....
Dear friends of Hyacinthos: A beautiful problem: Let ABC be a triangle, and draw isosceles triangles BCD;CAE;ABF externally to ABC, with BC;CA;AB as their...
Dear Riccardo ... If D,E,F lie respectively on the perpendicular bisectors of BC, CA, AB, obviously DEF and ABC are orthologic at O; hence your three lines ...
Dear friends, Let A'B'C' be the cevian triangle of the incenter I and let A"B"C" be its pedal triangle (intouch triangle) Let A* be the circumcenter of B'C'I...
Dear Eric, ... your locus is the union of : -- the line at infinity, -- a circular quintic without known (to me) centers on it, -- a circular circum-octic...
Dear Hyacinthos, I need a little help. If there is a triangle ABC with centroid G, how can I construct a circumhyperbola which center has a minimum distance ...
Dear Richard ... The nature of a circumconic with center W depends on the position of W wrt the sidelines of the medial triangle. If W0 is the projection of G...
Dear Jean-Pierre ... I don't know, is the distance between W0 and G the minimal possible distance from G to circumhyperbola's center W? Am I right? How can I...
Dear Hyacinthists, In Crux Vol. 13 (1987), p.153 there is a final comment to the problem in question (construct a triangle given HPO such that P belongs to the...
... Dear Jeff: I have seen your question to Bernard about the tool to dissect this kind of questions. I have write a notebook of Mathematica, Baricentricas.nb,...
... Dear Jeff: I have seen your question to Bernard about the tool to dissect this kind of questions. I have write a notebook of Mathematica, Baricentricas.nb,...
Dear friends, Obviously, 3) and 4) below represent the same configuration. The relationship with 1) is perhaps more interesting. It seems the circumcevian...
Let ABC be a triangle. Denote A1 = (Reflection of BC in AB) /\ (Reflection of BC in AC). B1 = (Reflection of CA in BC) /\ (Reflection of CA in BA) C1 =...
Dear Hyacinthos, Here's an interesting problem. It is easy to find a Heronian triangle that may be dissected into 3 Heronian triangles. But: is there a...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200516index.html The editors Forum...
ForumGeom
ForumGeom@...
Aug 23, 2005 8:51 pm
11469
Dear Antreas & Jeff, [APH] ... I think so as well, concurrence at your trilinear, {Sin[2^n A] / Sin[(2^n - 1) A] ::} Trilinear center of circle AnBC = {Cot[2^n...
Dear Peter ... Thanks for these results. In old problem discussions, you investigated variations with excentral etc triangles. So here, if AxBxCx is the...
In a triangle: cot(A/2) = (sinB + sinC) / (cosB + cosC) Here is a proof with trilinears. Lemma: Let ABC be a triangle, P = (x:y:z) in *actual* trilinears, and...
... every n. ... A]}. ... [APH] ... The circumcircle of the centers of the 3 circles AnBC, ABnC ABCn pass through the point of concurrence for n+1 It does...
Dear Peter ... How about the variation? A'1 := (Reflection of AoBo in BoCo) /\ (Reflection of AoCo in BoCo) Similarly B'1, C'1. Are the triangles ABC,...
Dear Jeff ... a ... on ... Construction of A' (cyclically for B', C') T = second intersection of the line BQ with the circle CPQ T'= second intersection of the...
Dear Jeff ... the ... with ... then ... particular ... a ... In my previous mail, I've noticed that A' = CT inter BT' where T is second intersection of the...
Dear Jean-Pierre, Thank you very much for your results in message 11474. I never noticed the construction you gave for triangle A'B'C' or the complex ...
