Dear Friends, I encountered a trivial property of the parabola, not found in my text books. It gives a very nice description of the parabolas circumscribing a...
Dear Paris This projective configuration of a conic through 3 points A, B, C and tangent at Q to a line (L) is very beautiful! I am sure there is a nice proof...
Dear All My Friends, Given triangle ABC and two points with barycentrics: P = (p : q : r), X = (x : y : z). B1 = reflection of B in PC B2 = reflection of B in...
Dear Eisso, François and Alexei ... such ... in ... angle ... imaginary ... the ... for ... Of course, there is a little problem because there are 4 common...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2008volume8/FG200804index.html The editors Forum...
ForumGeom
ForumGeom@...
Feb 4, 2008 4:27 pm
16100
Dear Paris and Francois! It seems that these problems were considered by Lev and Tatyana Emelyanoff. They presented the problems devoted to trypolars at Summer...
Alexey.A.Zaslavsky
zasl@...
Feb 5, 2008 7:33 am
16101
Dear Alexey Very interesting problem I had had to tackle when I was a young boy more than fifty years ago. I change your notation a little bit to avoid...
Dear Alexey If I name Db the harmonic conjugate of D wrt BB" and Da the harmonic conjugate of D wrt AA", then the tangent at C to the circumconic locus of P is...
Dear Francois! Thank you for your correstion. Of course the conic is inscribed on the triangle A0B0C0. Sincerely...
Alexey.A.Zaslavsky
zasl@...
Feb 5, 2008 9:52 am
16104
Dear Francois! 1 is the partial case of next general fact: if the pencil of conics determined by the points A, B, C, D is considered then the locus of poles of...
Alexey.A.Zaslavsky
zasl@...
Feb 6, 2008 1:48 pm
16105
Dear Alexey Cheer up! Thanks to your problem, it was true nostalgia for me! Friendly Francois ... [Non-text portions of this message have been removed]...
Hello Steve and other Hyacinthers, ... Steve, for the cubics curves, If you are interested, you can try to read my translation of the book of H. Durège " Die...
Dear Hyacinthists, d_k=internal angle bisector e_k=external angle bisector In this thread I would like to consider the following construction problems:...
Dear Alexey and Francois I was in leave last week and could not participate. I'll read your letters soon and think about. Thank you for your interest. Paris ...
Dear friends What is the locus of the points M with ABC-cevian triangle A'B'C' such that M is on the A'B'C'-circumcircle? In this case, notice that if : S(A')...
Dear Francois! I'm not sure that I understood correctly your problem. Is the triangle ABC given? If yes then A, B, C are diagonal points of cyclic...
Alexey.A.Zaslavsky
zasl@...
Feb 13, 2008 2:10 pm
16112
Dear Orlando, Ben_Grosso, Valentin and Hyacinthists, recently I read again some old message and particularly # 9541 and 9657 of 2004. Therefor, I propose a new...
Dear Alexey Yes the triangle ABC is given! So I am looking at points M which are on the circumcircle of their cevian triangle A'B'C' wrt ABC, i.e: M, A', B',...
Dear Francois, and Alexey If my computations are correct I think that your locus is the conic with barycentric equation aaxx + bbyy + cczz + (aa + bb + cc)(xy...
Dear Jean Louis Very nice proof! I need some precision on the french text: What do you mean by " I centre de ABC"? I guess you mean " I centre du cercle...
Dear Francois and Alexey, I said nonsense. The locus is a quintic. Best regards Nikos Dergiades ... ___________________________________________________________...
Dear Francois and Nikos! In my previous message I decided another problem. I understood that ABC is cevian triangle of M wrt A'B'C'. Sincerely...
Alexey.A.Zaslavsky
zasl@...
Feb 14, 2008 2:36 pm
16118
Dear All, If M and P are two points in the plane, I the middle of {M;P}; (d) the bisector of {M;P}is the locus of the center of circles through M and P These...
Dear Francois and Nikos! I said nonsense. The locus is a quintic. The equation of this quintic is a^2/x+b^2/y+c^2/z=a^2(y+z)+b^2/(z+x)+c^2/(x+y). Sincerely...
Alexey.A.Zaslavsky
zasl@...
Feb 14, 2008 2:37 pm
16120
Dear François and Hyacinthists I is the incenter of ABC. Sincerely Jean-Louis ... De : Francois Rideau <francois.rideau@...> À :...
Dear Alexey, 1) Could I have some concrete reference on Lev and Tatyana's presentation? 2) The theorem you proved with Arsenij is the old and classical way of ...
Dear All My Friends, Given triangle ABC, point X with barycentrics (x : y : z), point P with barycentrics (p : q : r). La is reflection of line XP in...
Dear Paris! The Emelyanov's paper was published (in Russsian) in "Matematicheskoe prosveschenije", 2002, N 6. May be it also was published in FG, but I amn't...
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