Dear Hyacinthians, X(1358) is defined in the current ETC as the Brisse-transform of X(101). I would like to present a new remarkable property of this point Let...
... Dear Eric How about if we replace the medial triangle with the Euler triangle? (ie the triangle formed with the midpoints of AH, BH, CH) ? Also, how about...
Dear friends, I have proved some(I guess)new results. Let we have H-orthocenter,G-centroid, K-symmedian or Lemoine-Grebe point, F1=X(13)-1st isogonic center or...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the Hyacinthos group. File : /solid.GIF ...
Hyacinthos@yahoogroup...
Jul 3, 2004 6:28 pm
9973
Dear Antreas, you wrote ... triangle? ... My sketches show that the Euler triangle does not produce a perspector. However I think I've found another...
Dear friends, I am sorry to be so inactive these days on Hyacinthos. Onfortunately I think this situation will not be changing soon, except perhaps in summer...
Dear Eric ... Thank you. Your wishes are very much appreciated. After your nice problems with incircle, I have this locus problem: Let ABC be a triangle, P, P*...
Let ABC be a triangle, P a point and PaPbPc the pedal triangle of P. The line PPa intersects AB, AC at Ab,Ac, resp The perpendicular bisectors of BAb, CAc meet...
Dear Floor, ... It's the Darboux cubic of triangle ABC. In fact, since the concyclic points A, B, C, A' give < A'BC = < A'AC = < PAC, and similarly < A'CB = <...
Dear Floor and Darij ... Let A*,B*,C* be the reflections of A',B',C' in BC, CA, AB and AA* /\ BC = A#, etc The triangles ABC, A*B*C* are perspective or the...
Dear Antreas, Floor and Darij, ... I find : a). ABC, A*B*C* are perspective iff P lies on the Jerabek hyperbola + Linf. b). A#,B#,C# are collinear iff P lies...
Dear Bernard, ... [BG] ... (...) ... ABC and A*B*C* are orthologic iff ABC and A'B'C' are orthologic naturally. So this does not come as a surprise! Kind...
Dear Antreas, ... I haven't checked your equation, but here is what I get: The lines AA*, BB*, CC* concur if and only if the point P lies on the line at...
Dear Floor, Darij and Bernard ... Let's see a variation: Denote: A' = the [other than P] intersection of the line PA and the circumcircle of PBC [instead of...
Dear Antreas,Nikos and all Greek friends For magnificient victory my sincere congratulations. Milorad R.Stevanovic [Non-text portions of this message have been...
... Dear Darij We can consider as reference triangle, the Euler triangle. That is: Let ABC be a triangle, A'B'C' the circumcevian triangle of O, and XYZ the...
Dear Antreas and Darij ... C'P ... If P' is the inverse of P in the circumcircle, your point is the harmonic conjugate of O wrt (P,P'); this point doesn't...
Dear Antreas and Jean-Pierre, Thanks a lot for the kind words about the IMO, you'd better wish me to get some nice geometry problems in the exams ;-) In...
Dear Milorad, thank you very much for your congratulations. Good luck also to Darij for the coming IMO. Greece now is on the peak of the European Football and...
Dear Nikolaos, ... I think that we can easily solve this problem if we suppose that <BFA' = w, <A'EC = w' using the following remarks. Let e and f be the fixed...
Dear Nikolaos and Jean-Pierre! ... and AC such as UP//f and VQ//e. ... I can propose next construction for the points E, F. Firstly we find the points P, Q...
Alexey.A.Zaslavsky
zasl@...
Jul 6, 2004 12:20 pm
9998
Dear Alexey and Nikolaos [ND] ... [JPE] ... respectively >on AB ... [AZ] ... find the ... o1 pass ... and Q and ... second ... respectively. Another possible...
... *** They are always perspective. The perspector has homogeneous barycentric coordinates Q = (u/(-S_Au^2 + S_Bv(w+u) + S_Cw(u+v)) : ... : ...). Here are...
Dear Antreas, [APH]: Denote: A' = the [other than P] intersection of the line PA and the circumcircle of PBC [instead of ABC] That is: Let ABC be a triangle...
Dear friends, I just realized that I was the lucky one who wrote message 10000 (and also 9999) on Hyacinthos. For the warm and fruitful communications here in...
Dear Paul ... Yes, they are always perspectice. I have posted it to my ANOPOLIS group, and have named the Transformation P --> Perspector as REHHAGEL...
Dear Paul and friends ... (and also ... half ... you concur ... Of course, I do. It was a very good and fruitful idea. Many thanks to all of you (and remember...
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.
