Dear Nik, [ND]: The point with barycentrics [(s-a)*(|a-b|-|a-c|)² : (s-b)*(|b-c|-|b-a|)² : (s-c)*(|c-a|-|c-b|)²] and search number 7.11040574869 I think is...
Alex, The Six Circles theorem comes from Evelyn, Money-Coutts and Tyrrell, 'The Seven Circles Theorem and Other New Theorems', London 1974, which contains a ...
Dear Paul, you are right. Although the point ((s-a)(b-c)^2 : (s-b)(c+a-2b)^2 : (s-c)(a-b)^2) lies on the Steiner in-ellipse my false is that in the product I...
Dear Nik, [ND]: Although the point ... *** I must have missed something. This point does not seem to the on the Steiner in-ellipse x^2+y^2+z^2-2xy - 2yz -2zx =...
... on the incircle. ... Q is an ... the line PQ and ... square of an ... product of the ... follows that if ... then ... Cute result - does it generalize to...
Dear Paul, sorry again, I meant the square point [(b-c)^2 : (c+a-2b)^2 : (a-b)^2 ] lies on the Steiner in-ellipse and my error was that I considered the point ...
Dear friends X(11) is the only polynomial point of degree 3 on the incircle The antipode X(1317) of X(11) and the second intersection P of the line ...
Dear Barry Wolk, [PY]> ... [BW] ... ***** It generalizies to all inscribed conics in ABC. If A',B',C' are the points of contact then the triangle A'B'C' is the...
Dear Hyacinthists, I think that there are only 4 polynomial centers of degree <= 5 on the incircle (in barycentrics) degree 3 : X(11) degree 4 : X(1317) and P...
Dear friends: Altought you know the proof by Aplication of Thebault's theorem (1) and Carnot's theorem(2), I send you a trivial proof of this theorem. Be ABCD...
Dear Jean-Pierre, thank you very much for these very interesting properties. I haven't yet given a proof. ... triangles is the union ... X(14)-X(16) ... common...
The great mathematician Harold Scott MacDonald Coxeter passed away. I am fwd-ing the following that was posted to math-fun list ______________________________ ...
Dear Friends, The book 'A Survey of Geometry', Revised Edn 1972 by Howard Eves features a cover logo of a triangle and its circumcircle with the diameters and...
A web page dedicated to Coxeter (in Spanish): http://www.personal.us.es/rbarroso/trianguloscabri/ Thanks to Ricardo Barroso Campos And a short note on...
Dear Nikolaos I'm sorry but it seems that my message has been shortened and that a part is lost. Here is the complete one. [JPE] ... [ND] ... I don't know but...
... theorem (1) and ... theorem. ... of ... points on BD ... on AC diagonal ... rectangle and ... hipotenuses and ... perpendicular to ... ra+rc=rb+rd ... ...
Dear friends, given a triangle ABC, if A'B'C' is the cevian triangle of P, then the circumcenter O of ABC is the orthocenter of A'B'C' for infinitely many...
Being offline for five days, I have been studying rather old problem fields, but I see that there may be open problems. A triangle center of a triangle is...
On the sides of a triangle ABC, describe equilateral triangles BCA+, CAB+, ABC+ (all outwards). Then we know that the circles BCA+, CAB+, ABC+ concur at the...
Dear Darij, ... Of course we may take for A+B+C+ also: * The third vertices of equilateral triangles pointed inwardly * The vertices of either of the Napoleon...
Dear Floor, ... And this is also part of my Schaal triangles theory, which I hope to re-examine later. It starts with the following well-known fact: Let ABC be...
Dear Darij, ... Yes, since condition (1) clearly is symmetric. ... Yes, I saw this in my sketches, too, and also that indeed the first and second Napoleon...
There are lots of concyclicities related to this. Using the notation A* for reflection of vertex A in side BC, and A+ and A- as before, we have that AA+A-A*...
Lawrence Evans
75342.3052@...
Apr 5, 2003 4:45 pm
6879
In a prior message I commented that configurations having circles instead of lines occur in the sort of exploration that Darij mentioned. This might be of...
Lawrence Evans
75342.3052@...
Apr 5, 2003 10:18 pm
6880
Dear friends, consider two circles C1 and C2, externally tangent at O and two points A and B on C1 and C2 resp. for which positions of A and B the area of...
Dear Darij and other Hyacinthists if W = Warnau point and W' = second Warnau point (starting with the second Fermat point), then W and W' lie on the Neuberg...
Dear Jean-Pierre Ehrmann, LOTS OF THANKS FOR THE BARYCENTRICS !! I have tested them in the 6-9-13 case, they are correct. The search number (in actual...
Having problems with message search?
Fill out this form to ensure your group is one of the first to be migrated to the new message search system.
