Dear Hyacinthists, As some of you already know I am writing a book on triangle constructions. I have already published in French in 1996 a book on this...
15998
jpehrmfr
Jan 8, 2008 4:27 pm
Dear Armpist and Cosmin ... Using this remark, it becomes obvious to find the second circle (O') touching the 6 Thebault circles : The three radical axis of...
15999
Alexey.A.Zaslavsky
zasl@...
Jan 9, 2008 1:32 pm
Dear Francois! What are the Malfatti squares? Sincerely Alexey Dear friends Points B and C are given in the plane. What is...
16000
Alexey.A.Zaslavsky
zasl@...
Jan 9, 2008 1:32 pm
Dear Michel, Francois, Jean-Pierre and other colleagues! Ten years ago I proposed for Moscow mathemathical olympiad next problem: Prove that the projection of...
16001
Son Hong Ta
dam_xoan90
Jan 9, 2008 1:32 pm
... touching ... (note ... point ... 2r) - ... Dear Jean-Pierre, Cosmin and all, Your first result above was mentioned and proved by Nguyen Minh Ha in a...
16002
Cosmin Pohoata
pohoata_cosm...
Jan 9, 2008 2:33 pm
Dear Son and Armpist, Thank you both for the references to the particular cases. Son, does Nguyen Min Ha mentiones anything about the general configuration in...
16003
jan.vonk
Jan 10, 2008 12:06 am
Dear Hyacinthists, I believe the following results are true: Let ABC be a triangle and call A'B'C' it's first Neuberg triangle (i.e. the triangle formed by the...
16004
Son Hong Ta
dam_xoan90
Jan 10, 2008 1:23 pm
... the ... Dear Cosmin, He only mentioned about the congurence of the Thebault circles in the Nagel case. I've read this paper again, and in this paper, he ...
16005
Francois Rideau
francoisrideau
Jan 10, 2008 2:56 pm
Dear Jeff and dear friends Start with uniform motions t -->a(t), t -->b(t), t b--> c(t) on the sidelines. Then we get one to one affine maps: a(t) <--> b(t)...
16006
Francois Rideau
francoisrideau
Jan 10, 2008 2:57 pm
Dear Jeff and dear friends You are right about Cheyenne, a character in the Sergio Leone movie: Once upon a time in the West. Of course, I like this movie and...
16007
Jeff
jbrooks_update
Jan 10, 2008 2:57 pm
Dear Francois, [FR] Of course this configuration is well known. Looking at the position of the choo-choos at time t = 0 and time t = 1, we get 3 pairs: (a(0),...
16009
garciacapitan
Jan 10, 2008 9:13 pm
Dear Jan, all your conjectures are true, I have checked them using barycentric calculations. The barycentric coordinates of P and P', not in ETC, P = {-7 a^6...
16012
jan.vonk
Jan 10, 2008 10:16 pm
Dear friends and Garcia, Many thanks to Garcia Capitan for his verifications. The calculations were just too complex for me. I have noticed some other results...
16013
jan.vonk
Jan 11, 2008 11:58 am
Dear Hyacinthists, I would like to add some more results: Note that 9) expresses that LMN and the excentral triangle of XYZ have parallel sidelines. Therefor,...
16014
Luís Lopes
qedtexte
Jan 11, 2008 9:05 pm
Dear Hyacinthists, e_b = external bisector How many different solutions can this problem have? Best regards, Luis ...
16015
Son Hong Ta
dam_xoan90
Jan 12, 2008 3:46 pm
Dear Hyacinthos, When trying to prove a problem, I noticed that the following problem is true: Let ABC be a triangle and P be an arbitrary point on its plane....
16016
garciacapitan
Jan 12, 2008 8:19 pm
We can find a proof of Jacobi theorem at http://www.mathlinks.ro/Forum/viewtopic.php?p=186725#186725 Has anybody, in addition, some historical references of...
16017
Francois Rideau
francoisrideau
Jan 12, 2008 8:19 pm
Dear Son You have some problems with your notations. Let R your starting point and S your final concurrency point. Let XYZ be the orthic triangle of ABC and...
16018
Eric Danneels
efn4900
Jan 12, 2008 8:19 pm
Dear Son Hong Ta, your perspector is the midpoint of P and the X(4)-Ceva conjugate of P Kind regards, Eric ... problem ... Let D, ... respectively. ... to BC...
16019
jan.vonk
Jan 12, 2008 9:38 pm
Dear Son, Francois and Eric, ... I think you're a good drinker, because this is a very nice remark. It's easy to see why it is true: Because of the definition...
16020
Cosmin Pohoata
pohoata_cosm...
Jan 12, 2008 9:38 pm
Dear Francisco Javier, See here the nicest proof of the `Jacobi theorem` (in my opinion): http://www.mathlinks.ro/Forum/viewtopic.php?p=870445󔠭. It is ...
16021
Francois Rideau
francoisrideau
Jan 13, 2008 3:55 pm
Dear Cosmin I have read Kostas Vistas proof using radical axis. It is wonderful. I noticed that in english text, one often uses the notation: <PQR for angles,...
16022
Son Hong Ta
dam_xoan90
Jan 14, 2008 12:23 pm
Dear Eric, Francois, and Jan Thank you for your interest, comments, and solutions. Friendly, Son....
16023
Francois Rideau
francoisrideau
Jan 14, 2008 12:24 pm
Dear Cosmin I correct here a little mistake. Of course, it is Kostas Vittas (and not Vistas!), who gives us this wonderful proof of the Jacobi theorem. In the...
16024
Alexey.A.Zaslavsky
zasl@...
Jan 14, 2008 12:56 pm
Dear Son and other colleagues! Similar problem was proposed at first geometrical olympiad (2005). Let H be the orthocenter of triangle ABC and X an arbitrary...
16025
ForumGeom
ForumGeom@...
Jan 14, 2008 4:28 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2008volume8/FG200802index.html The editors Forum...
16026
anthonycharlesmichael
anthonycharl...
Jan 15, 2008 1:08 pm
... can be ... circles ... altitudes, and ... Interesting result! I think there is a relative result. If we consider an arbitrary point P, let Ba and Ca are...
16027
Cosmin Pohoata
pohoata_cosm...
Jan 15, 2008 1:08 pm
Dear Quang Tuan Bui and others, Some questions inspired by your paper in Forum Geometricorum 8 (2008) 7--12: 1) On the orthocenter configuration (I will change...
16028
anthonycharlesmichael
anthonycharl...
Jan 15, 2008 1:53 pm
... (easy to prove) ObOb' = OcOc', where Ob', Oc' are the orthogonal projections of Ob, Oc on AB, respectively, AC (figure 5 from your paper). ... I don't...
16029
Pohoata Cosmin
pohoata_cosm...
Jan 15, 2008 2:48 pm
Dear Michael and others, Sorry for the confusing exprimation. Indeed, I was wondering that, if Ca, Cb, Cc are the circles for a point P from the locus...
