Dear friends I have noticed that the Nikos configuration in message 6466 was simply the figure of the special Sondat theorem that is to say 2 orthologic...
Dear friends Now the special Sondat theorem has been proved thanks to Darij, it remains to prove the general Sondat theorem always in a synthetic way. That is...
Hello everyone, I only know of 2 cataloged inscribed parabolas: the Kiepert and Yff parabolas with perspectors :1/(cc-aa): and : 1/(c-a) :. The affine methods...
To all, Sorry I have been away. I keep trying to finish the subject of conics and move on but they keep giving me reasons to look at them. Likewise I want to...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2006volume6/FG200627index.html The editors Forum...
ForumGeom
ForumGeom@...
Oct 2, 2006 2:49 pm
14225
Dear all, In reading "Another approach to the trisection problem" in The Mathematical Gazette, Vol 90, #518, July 2006, pp. 280--283, Note 90.38, there is a...
[LL] ... Dear Luis Geometry History is not off-topic! In JFM I found this paper of A.C. (the only one listed) Cohn, A. : Ueber die Anzahl der Wurzeln einer...
Dear Antreas, Thank you for your kind reply. I said off topic because I don't know what A.C wrote about. The mentioned theorem is of an algebraic/number theory...
Dear friends It is well known that 2 triangles ABC and A'B'C' are perspective if and only if there exist some conic {Gamma} (real or not) such that ABC and...
Dear Francois ... and only ... A'B'C' are ... Are you sure? I think that the correct statement is : Two triangles are conjugate wrt a same conic if and only if...
Dear François, ... The line AA' meets BC at A'1 and B'C' at A1. The involution on AA' which swaps A & A1, A' & A'1 has two fixed points M & M' which must lie...
Dear Francois [FR] ... if ... and ... [JPE] ... 6 ... I'm sorry; I thought that you were meaning : ABC and A'B'C' are selfconjugate wrt a conic. Of course,...
Dear Bernard and Jean-Pierre Thanks for your swift answer. Now it's up to me to get the macro! Friendly François [Non-text portions of this message have been...
Dear friends: I have found the nice fact: Let ABC be acute triangle, with NPC (O_9). Draw the small circle (O_a) tangent to AB,AC and (O_9), with the touch...
Dear Juan Carlos ... (O_a) ... Maybe, I've missed something but this relation is only due to the fact that AAb = AAc,... (it is not necessary to have three...
Dear friends Now fed up with orthology, gimme some parallelogy to think about! So I have a new riddle for you. Given 2 triangles ABC and A'B'C', find all...
Dear All My Friends, The line X(2)X(31) cuts the line X(10)X(1104) at a point with barycentrics: 2*a^3 + b^3 + c^3 : : Search value: +2.10759557730198 not in...
Quang Tuan Bui
bqtuan1962@...
Oct 6, 2006 8:44 am
14237
Dear Tuan, It is the complement of the complement of X(31), or the complement of X(2887), (b^3 + c^3):. The complement of a^n:: is (b^n + c^n):: The complement...
Let ABC be a triangle with BC := a (fixed), and A' := the orthogonal projection of A on BC. R, Rb, Rc := the circumradii of the triangles ABC, A'BA, ACA, resp....
Dear Antreas, [APH]: Let ABC be a triangle with BC := a (fixed), and A' := the orthogonal projection of A on BC. R, Rb, Rc := the circumradii of the triangles...
Let ABC be a triangle with BC := a (fixed), and A' := the orthogonal projection of A on BC. R, Rb, Rc := the circumradii of the triangles ABC, A'BA, A'CA,...
Dear Antreas ... the locus is not only the obvious circle with diameter BC but also the rectangular hyperbola with center the mid point of BC foci on BC that...
Dear Antreas and Nik, [APH]: Let ABC be a triangle with BC := a (fixed), and A' := the orthogonal projection of A on BC. R, Rb, Rc := the circumradii of the...
Dear friends I give you some hints: 1° It is equivalent to find the loci of O and O' such that: lines AO and A'O' are parallel, lines BO and B'O' are...
Dear Francois [FR] ... the pairs ... (U',O' ) the ... and O', in ... needed! I haven't looked very closely at your problem (I mean that that I haven't proved...
Dear All My Friends, Given triangle ABC, two points P, U with barycentrics: P = (p : q : r), U = (u : v : w) and circumcircle (O). Let fourth intersection...
Quang Tuan Bui
bqtuan1962@...
Oct 7, 2006 10:27 am
14246
Thanks Jean-Pierre. In fact I have an analytic solution but I am not still satisfied with my synthetic one, so every idea would be welcome. Let notice some...
Dear friends Following an idea of Mark, given a triangle ABC, I tried to construct a triangle A'B'C' orthologic and perspective with ABC, (i.e: bilogic with ...
Dear friends In my previous post, I ask: What is the locus (if any) of the point P such that if lines AP, BP, CP cut again the ABC-circumcircle respectively in...
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