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...
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...
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 ...
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 ......
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...
... 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...
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...
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...
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...
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...
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...
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...
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...
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 ...
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...
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 ...
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...
Dear friends ... [JPE] ... one ... going ... perpendicular ... mapping ... UbVb; ... Here is a more symetric way to draw this figure : Ca is the circle going...
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...
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-->...
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...
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...
sorry, I forgot *Discussions: Relating to the "Simson Line" or "Wallace Line"* Roger A. Johnson *The American Mathematical Monthly*, Vol. 23, No. 2 (Feb.,...
Dear friends ... it ... Robert ... I quote Roger A. Johnson in Modern Geometry : << In the nineteenth century, it was generally supposed that this theorem was...
... Jean-Pierre, Thanks. I used to call these "polar conics" but Conway has me calling them "diagonal conics." Terminology...ug! Since the incircles are...
Dear Steve [Steve] ... parallel ... [JP] ... asymptots of ... precevian ... the ... [Steve] ... Because they have a diagonal matrix?? Let L1,L2 be the infinite...
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