... HP. ... CC* (resp.) ... I'm sure the fact that the Simson line of P' is parallel to HP helps, but it's 4 AM here (in Romania), so I'm going to think it...
... helps, ... In fact, the following holds (easy to prove, just a quick angle chase): If ABC is a triangle and M is a point on the circumcircle of ABC then ...
... BC, ... K. ... (1): The intersection point is the centroid of the perimeter of triangle ABC. It's the well-known Spieker center (X(10)). The fact that it's...
Dear "ben_goss_ro" (= grobber at MathLinks?), ... This puzzles me a bit. In fact, the lines MM_1, NN_1, PP_1 do bisect the perimeter of triangle ABC, but the...
... Hi! Yes, I am grobber (:)). About the first part of the problem: I apologize for not completing it. No, not all the lines which bisect the perimeter pass...
... For (a): We can see that triangle (B'C'A') is obtained from (ABC) by a rotation of -60 degrees followed by a translation, and because if we compose a...
Dear Darij and "ben-gross-ro" ... Consider the parabola Pa with focus the excenter Ja, touching AB and AC at the same points than the A-excircle, then a line...
Dear Darij, [DG]: ... but I am still searching a better ... This is clear if you think in terms of barycentric coordinates. The perimeter of ABC is equivalent...
Dear all who replied to my query about X(10) as the centroid of the perimeter in Hyacinthos message #9628: Thank you a lot! However, I must admit that my...
Dear friends, I just found out from ETC that the center of the Lester circle, X(1116) lies on the line joining the centers of the Kiepert and Jerabek...
Dear Paul ... circle, ... The line joining your two centers is the perpendicular bisector of X (13)X(14). In the same kind of idea, if N = NP-center and U,U'...
Dear Jean-Pierre, [PY]: I just found out from ETC that the center of the Lester ... *** Thank you very much, Jean-Pierre. Is there an easy way of explaining ...
Dear Paul, and Jean-Pierre another explanation more complex but with interesting properties_questions is the following. X(115) = Center of Kiepert hyperbola ...
Dear friends! Sa = (b^2+c^2-a^2)/2 = 2ScotA (S - area of triangle ABC), Sb and Sc are defined in the same way. q= y^2 (x+z)^2; Q = y^2 (Sa*x^2 + Sc*z^2) - b^2...
alex
alex_geom@...
Apr 7, 2004 11:10 am
9642
Dear friends, Given a point P with cevian triangle XYZ, find an elegant geometric construction of a point Q such that the intersections of AQ with YZ, BQ with...
Dear Paul ... geometric ... to ABC. Here is a possible construction - probably not the best one - For any point Q, let L(Q) be the line joining (BQ inter ZX)...
Dear Paul and Jean-Pierre! ... I think that the simplest construction is the next. The lines passing through A,B,C and parallel to YZ, ZX, XY form the triangle...
Alexey.A.Zaslavsky
zasl@...
Apr 9, 2004 8:37 am
9645
(cross poted to Historia Mathematica) Dear friends! In his essay "Die Geometrische Constructionen augef"uhrt mittelst der gerade Linie und eines festes ...
As you might know, I am one of the 16 participants of the German IMO training 2004 (what doesn't necessarily mean I will be at the IMO). Additionally to the ...
Hello All, In reference to Dick Klingens question about "Herr Prof. Dove", I did a quick search at Google.de and found out the following: Surname: Heinrich...
Dear Darij, you wrote: I have not succeeded yet to solve Problem III.1; From the PROBLEM SET III by MARTIN HÄRTERICH III.1. Let the equilateral triangle...
Dear all Today I was scanning some old Zbl (Zentralblatt reviews) whence I found following excellent book on orthopoles. It’s as follows: Pedal lines,...
Dear Nikolaos, ... Somehow I don't find the error in my coordinates, unless there is an error in my barycentrics of X(396) what would be quite strange. ... ...
Dear Darij, you write ... Your problem is a nice application of the technique used by Hadamard in his famous geometry textbook in connection with the Ptolemy...
Dear Vladimir, ... Thanks - this was really nice! I had in mind the following proof: The area S of the quadrilateral ABCD is 1/2 * ef * sin t, where e and f...
Dear Darij, you wrote ... Surprisingly, the assumption that O lies inside V seems to be essential! By a computer experiment based on some preliminary...
Dear Vladimir, ... Well, this was my surprise, too! ... Thanks - on my sketch, the point seems to exist, too. On the other hand, I don't see any possibility to...
... D. ... Denote ... This was used in a Romanian TST in 2002. Only one student solved it (some of you might have heard of him: Valentin Vornicu, the ...
