The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201214index.html The editors Forum...
21047
Barry Wolk
wolkbarry
Jun 1, 2012 8:01 pm
... Let t1=sqrt((c+a-b)(a+b-c)), t2=sqrt((a+b-c)(b+c-a)), t3=sqrt((b+c-a)(c+a-b)), with t1,t2,t3 all > 0. Then P=(a-t1, b-t2, c-t3), A'=(a-t1, b+t2, c+t3),...
21048
Nikolaos Dergiades
ndergiades
Jun 1, 2012 10:33 pm
Dear friends, [Randy Hutson] ... [Barry Wolk] ... [Randy Hutson] ... If the isotomic conjugates of the persectors of two inconics are interior points of ABC...
21049
Randy Hutson
rhutson2
Jun 4, 2012 2:01 pm
Thanks Barry and Nikos. I love it when these problems have such elegant solutions. Best regards, Randy Hutson ... [Non-text portions of this message have...
21050
Alexey Zaslavsky
zasl@...
Jun 6, 2012 9:52 am
Dear colleagues! Is next fact known? Let P, Q be two point on the circumcircle of triangle ABC. Then their Simson lines meet on the altitude from C iff PQ is...
21051
forumgeom forumgeom
ForumGeom@...
Jun 6, 2012 12:40 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201215index.html The editors Forum...
21052
Daniel
dvacaretu
Jun 6, 2012 5:02 pm
Yes, it is a particular case of S-triangles. Two triangles ABC and A'B'C' inscribed in the same circle are S-triangles iff arc(AA')+arc(BB')+arc(CC')=0 (mod...
21053
Nikolaos Dergiades
ndergiades
Jun 6, 2012 6:03 pm
Dear Daniel, Very good observation and proof. So we can generalize Alexey's problem as follows: If L is a line and S is the isogonal conjugate of its infinite...
21054
Cosmin
pohoata_cosm...
Jun 7, 2012 4:32 pm
An easier proof would be to just recall that the Simson line bisects the segment determined by the orthocenter of the triangle and the point, thus if we let X,...
21055
Barry Wolk
wolkbarry
Jun 7, 2012 7:33 pm
... A routine calculation using complex numbers as coordinates gives the following: If A,B,C,D,E are on the unit circle, then the Simson lines of D and of...
21056
Alexey Zaslavsky
zasl@...
Jun 8, 2012 6:52 am
Dear Daniel, Nikos, Cosmin and Barry! Yes, I also found these general facts. Thank you for the references. Also the envelop of Simson lines is the astroid and...
21057
Bernard Gibert
bernardgibert
Jun 8, 2012 7:01 am
Dear Alexey, ... see K024 in http://bernard.gibert.pagesperso-orange.fr/Exemples/kjp.html Best regards Bernard [Non-text portions of this message have been...
21058
Alexey Zaslavsky
zasl@...
Jun 8, 2012 7:59 am
Dear Bernard! see K024 in http://bernard.gibert.pagesperso-orange.fr/Exemples/kjp.html Thank you. Sincerely Alexey [Non-text...
21059
Jean-Louis Ayme
jeanlouisayme
Jun 14, 2012 5:25 am
Dear Hyacinthists, I have read that a result of Droz-Farny is associated with the name of NOYER. Who is Noyer? Where can I find some informations about it?...
21060
Chris Van Tienhoven
chris.vantie...
Jun 15, 2012 8:31 pm
Dear Friends, I noticed there are all kind of centers, lines, conics, cubics, etc. in a Complete Quadrilateral/Complete Quadrangle. So I started writing a...
21061
Chandan Banerjee
cbanerjee.2011
Jun 18, 2012 8:15 am
I have posted a synthetic solution(given by me and Sayan Mukherjee) of the Neuberg problem here:- http://www.artofproblemsolving.com/blog/71562 Can you refer...
21062
Angel
amontes1949
Jun 18, 2012 5:58 pm
Dear Hyacinthists, Barycentric coordinates are used in respect of a triangle ABC. Let P=(u:v:w) be a point not on a sideline of ABC and let d=(p:q:r) be a line...
21063
forumgeom forumgeom
ForumGeom@...
Jun 21, 2012 3:35 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201216index.html The editors Forum...
21064
mbabelian
Jun 22, 2012 8:17 pm
Dear all how can i find the proof of these results,17 circles concure,? please put the proof or if the proof is already exist here,put the link or address. ...
21065
Chandan Banerjee
cbanerjee.2011
Jun 23, 2012 5:44 am
Like Quang Tuan Bui mentioned, all the circles in the message except O1,O2 are well-known. So here are the proofs for O1,O2. Its well-known that if V is the...
21066
mbabelian
Jun 23, 2012 6:49 am
thank you so much Chandan Banerjee, i will be gratify if u put the solution of the cevian and pedal circle of arbitrary point P and the nine points circle....
21067
Jean-Louis Ayme
jeanlouisayme
Jun 24, 2012 9:17 am
Dear Hyacinthists, working again on the Droz-Farny line, it would be nice if somme of You have access to these references 1. Droz-Farny A., Question 14111,...
21068
John Sharp
sliceforms
Jun 24, 2012 4:07 pm
Jean-Louis There are many volumes of Mathesis and Mathematical Questions from the Educational times at The Internet Archive http://archive.org/ and on Google ...
21069
Jean-Louis Ayme
jeanlouisayme
Jun 26, 2012 9:21 am
Dear Hyacinthists, an article concerning “La droite de Danneels’’ or ‘’Danneels’s line’’ has been put on my website with original proofs. ...
21070
Chris Van Tienhoven
chris.vantie...
Jun 26, 2012 5:47 pm
Dear Friends, I got some very nice remarks following my announcement of the Encyclopedia of Quadri-Figures. Seiichi Kirikami attended me on a special property...
21071
forumgeom forumgeom
ForumGeom@...
Jun 27, 2012 2:07 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201217index.html The editors Forum...
21072
John Sharp
sliceforms
Jun 27, 2012 4:21 pm
Jean-Louis I have found your reference to Noyer, p 39 of Journal de mathématiques spéciales 1893 the web link at the Internet archive is ...
21073
Francisco Javier
garciacapitan
Jun 27, 2012 5:58 pm
[JS] The best way to download the PDF is not to do it from the list at the left but to first choose read online then at the top right choose the i symbol and...
21074
Jean-Louis Ayme
jeanlouisayme
Jun 28, 2012 12:10 pm
Dear Mathlinkers, continuing some investigations on the end of the XIXe century, where can I found a short biograpy of G. C. Boubals? Sincerely Jean-Louis ...
21075
Angel
amontes1949
Jun 29, 2012 5:04 pm
Dear Chris van Tienhoven, I have a Quadrangle Center that is not currently in EQF. Let P1, P2, P3, P4 be the defining Quadrangle Points. Let S1 = P1.P4 /\...
