Let ABC be a triangle and A'B'C' the cevian / pedal triangle of a point P. Denote: Ab, Ac:=The orthogonal projections of B',C' on PC',PB', resp. A":= B'C' /\...
Dear Antreas: For the pedal triangle of P: a) AbAc, BcBa, CaCb are concurrent only if P is on the sidelines or the line at infinity b) A",B",C" are collinear...
Dear Antreas, ... Yes, you are right! In fact, we can say more: The three triangles share the same circumcenter. It's the Spieker point Sp of ABC. ... Here's a...
Let ABC be a triangle, P,P* two isogonal conjugate points,and A'B'C' the pedal triangle of P. La,Lb,Lc := the parallels to PP* through: 1. A,B,C or 2. A',B',C'...
I am not sure if I have already posted this; anyway here is it: Let ABC be a triangle, HaHbHc, MaMbMc the orthic, medial triangle, resp. A1B1C1 := The...
Dear Jeff, I once figured out next method for finding out the 4th intersectionpoint S4 of any circum-conic with the circumcircle. I suppose 2 other points P1...
Let ABC be a triangle, and AgBgCg, AkBkCk the cevian triangles of the isogonal conjugate points G,K, resp. Denote: a,b,c := The cevian lines of G (ie the lines...
... Dear Haycinthists, A general method for finding the intersection points of any two conic sections, given 2 or 3 of these common points is here : ...
Lemma : Notation : (X) means the circle with circumcenter X Let (1),(2),(3) be three concurrent circles at a point P. Let Q be the circumcenter of the triangle...
It is simpler than I thought at first glance! [APH] ... Let S = PQ /\ 1QP1 In the triangle (1 1Q P1) with transversal PQS we get (by Menelaus Theorem ) that S...
Here are 4 archimedean circles by construction: Let ABC be an equilateral triangle of side 1, and A',B',C' three points on BC,CA,AB, resp. such that: BA' = CB'...
I have a problem in identifying a number of points in work I am doing. I am generating lots of points and wish to know of their existence in the ETC. I want a...
Dear Chris, First, thank you very much. I had long suspected the inverse in the circumcircle could be used (based on algebraic observations) but, I could not...
Dear Antreas, I am so sorry, I forgot to give the link: http://surveylink.yahoo.com/wix/p6290938.aspx Sincerely, Jeff ________________________________ From:...
Dear Jeff, ... Dear Jeff, I am glad to hear this is what you were looking for ! I found this constructing from the question how to construct centers X98-X112...
Thanks for pointing this out Francisco I never look at the top of the ETC page since I always look at the content on the page and saw the triangles as...
Dear Francisco Thanks [APH] ... [FGC] ... I think that the most interesting case is: (pedal triangle - incircle): We have here Golden Arbelos: A',B',C' divide...
Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P. The reflections of B'C',C'A',A'B' in AP,BP,CP, resp. intersect BC,CA,AB in A",B",C",...
[APH] ... [APH] ... ^^^^^^^^^^^^^^ I meant to say case of perpendicular lines at A',B',C' (Triangle T2) ... BTW, I think that we have another one similar...
Let ABC be a triangle and P a point. We draw through P: 1. The parallels to AB, AC or 2. The perpendiculars to AB, AC or 3. The parallels to the sides HaHb,...
Dear Chris, ... I like Mathematica because you can both import and export data from it. Autocad was useful to me for a while because it also has this...
Dear Jeff and Chris I think the Chris construction is rather tedious. The idea is that if you transform a circumconic by isogonal conjugation, then you get a...
Note that in this way, each vertice A, B, C gives a line on D. So D is at the meet of these 3 lines and it's a 1st degree as expected! Friendly Francois ... ...
Let ABC be a triangle and A'B'C' the pedal triangle of P. Let (Ab), (Ac) be the Arcimedean twin circles of the arbelos (BC,A') [ inside the triangle]. ...
I read the following problem in Tran Quang Hung¢s Geometry blog http://analgeomatica.wordpress.com/open-problems/ Problem 3 [my rewording partly]. Let ABC,...
Dear Antreas ... The six Simson's lines of A', B', C' wrt ABC and of A,B,C wrt A'B'C' concur at the center of the Taylor circle of A*B*C*. Your circle is...
Let ABC be a triangle and Ab,Ac the Orthogonal projections of A on the Reflections of BH,CH in AO, resp. Let La be the reflection of the Euler Line of AAbAc in...
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