Dear All My Friends, Given triangle ABC with circumcircle (O). There is and exactly one equilateral triangle inscribed in (O) taken A as one vertex. We denote...
14936
michgarl
Mar 2, 2007 5:22 pm
Je reviens sur le sujet traité dans les messages 10135,10136,10146 et 10358. Après avoir pris conaissance des résultats de Darij Grinberg, je me suis...
14937
garciacapitan
Mar 2, 2007 5:38 pm
Dear friends, I would like to have a construction of the point (0:a^2-2(b+c)a+b^2+c^2:-2bc) Thank you....
14938
Paul Yiu
yiuatfauedu
Mar 2, 2007 8:44 pm
Dear Tuan, How wonderful. I make a quick sketch and see that your P is the isogonal conjugate of the infinite point of the Euler line. Best regards Sincerely ...
14939
Francois Rideau
francoisrideau
Mar 2, 2007 9:18 pm
Anh Tuan oi I think the point P is known for a long time. It is X(74). It was found by Dobbs more than 100 years ago with just your way! Friendly François ......
14940
Andreas P. Hatzipolakis
xpolakis
Mar 2, 2007 9:38 pm
Dear Tuan and Paul Since there are no "islands" in the Geometry "sea", I am wondering how can we generalize it. Probably a way is this: Let ABC be a triangle...
14941
pneagoe
Mar 2, 2007 9:52 pm
... one equilateral triangle inscribed in (O) taken A as one vertex. We denote its bottom line wrt A as La, intesection of La with sideline BC as A'. Similarly...
14942
Francois Rideau
francoisrideau
Mar 3, 2007 12:07 am
Anh Tuan oi As Paul notices, your P is X(74) wrt ABC. To prove the last property of the line A'B'C', I think the best is to use polarity wrt the imaginary...
14943
Steve Sigur
steve_sigur
Mar 3, 2007 12:20 am
Sorry I got circum and inconics mixed up. Here is the correct message. Bernard wrote this in Hyacinthos a few years ago. ... I was wondering how one shows...
14944
pneagoe
Mar 3, 2007 12:54 am
Dear Andreas, Let ABC be a triangle with circumcircle C(O) and the incircle c(I). Ca is the circle with center A and radius AI. La is the radical axis of the...
14945
Steve Sigur
steve_sigur
Mar 3, 2007 12:57 am
Bernard wrote this in Hyacinthos a few years ago. ... I was wondering how one shows this. This result combines with one of my own to give this Every...
14946
pneagoe
Mar 3, 2007 1:25 am
Dear Andreas, If the points A', B', C' lies on the line L and the lines AA", BB", CC" are concurrent at P then : 4. the point P lies on the line OI. 5. OI and...
14947
Paul Yiu
yiuatfauedu
Mar 3, 2007 2:01 am
Dear friends, BQT (14935) Given triangle ABC with circumcircle (O). There is and exactly one equilateral triangle inscribed in (O) taken A as one vertex. We...
14948
Quang Tuan Bui
bqtuan1962
Mar 3, 2007 2:28 am
Dear All My Friends, Thank you very much for your references and remarks. I have some results: - L bound with ABC one complete quadrilateral with Miquel point...
14949
jpehrmfr
Mar 3, 2007 7:41 am
Dear Steve ... The axes of the inconic with center M are parallel to the asymptots of the conjugate rectangular hyperbola going through M (ie the rectangular ...
14950
Quim Castellsaguer
fqces
Mar 3, 2007 11:32 am
Dear friends, I have read in "American Mathematical Monthly", may 2006, this result: "Any inscribed triangle UVW is similar to the cevian triangle of a point...
14951
jpehrmfr
Mar 3, 2007 11:35 am
Dear friends [QTB] ... one equilateral triangle inscribed in (O) taken A as one vertex. We denote its bottom line wrt A as La, intesection of La with sideline ...
14952
jpehrmfr
Mar 3, 2007 11:57 am
Dear Quim ... This is not possible with ruler and compass : look at the case UVW equilateral; there exists usually 4 or 6 equilateral cevian triangles, none of...
14953
jpehrmfr
Mar 3, 2007 12:54 pm
Dear friends ... [JPE] ... one ... going ... perpendicular ... mapping ... UbVb; ... Here is a more symetric way to draw this figure : Ca is the circle going...
14954
jpehrmfr
Mar 3, 2007 1:42 pm
Dear friends I wrote ... the ... this ... a ... then ... In fact, this is a bit tedious because the centers of the three circles Ca, Cb, Cc are homothetic in...
14955
Francois Rideau
francoisrideau
Mar 3, 2007 3:09 pm
... And what about the conic locus of the point BU' inter CW' through B and C? ... . ... [Non-text portions of this message have been removed]...
14956
Francois Rideau
francoisrideau
Mar 3, 2007 3:20 pm
Sorry, I send my post by mistake! I only want to say that this problem is a special case of the following: That is to say, given 3 homographic motions t-->...
14957
Nikolaos Dergiades
ndergiades
Mar 3, 2007 3:30 pm
Dear Quim, ... As Jean-Pierre said, P is conic constructible, and the construction of the conics is the following: Let A'B'C'= UVW be the triangle inscribed in...
14958
Aleksandra.Wojtas@...
aleksandraali
Mar 3, 2007 3:49 pm
I'm looking for some information which I need to my thesis. I'm going to put there something about Simson Line. And while the theorem and the proof was not so...
14959
Ricardo Barroso
ricardobca
Mar 3, 2007 4:00 pm
Dear Aleksandra please .. author, title, review, of article? Ricardo Barroso ... De: "Aleksandra.Wojtas@..." <wojtas.ola@...> Para:...
14960
Aleksandra.Wojtas@...
aleksandraali
Mar 3, 2007 4:29 pm
sorry, I forgot *Discussions: Relating to the "Simson Line" or "Wallace Line"* Roger A. Johnson *The American Mathematical Monthly*, Vol. 23, No. 2 (Feb.,...
14961
jpehrmfr
Mar 3, 2007 4:33 pm
Dear friends ... it ... Robert ... I quote Roger A. Johnson in Modern Geometry : << In the nineteenth century, it was generally supposed that this theorem was...
14962
Ricardo Barroso
ricardobca
Mar 3, 2007 5:30 pm
Dear Hyacinthos The article of Johnson Ricardo ... De: "Aleksandra.Wojtas@..." <wojtas.ola@...> Para: Hyacinthos@yahoogroups.com Enviado: sábado,...
14963
Steve Sigur
steve_sigur
Mar 3, 2007 6:51 pm
... Jean-Pierre, Thanks. I used to call these "polar conics" but Conway has me calling them "diagonal conics." Terminology...ug! Since the incircles are...
14965
jpehrmfr
Mar 4, 2007 4:09 pm
Dear Steve [Steve] ... parallel ... [JP] ... asymptots of ... precevian ... the ... [Steve] ... Because they have a diagonal matrix?? Let L1,L2 be the infinite...
