Dear Antreas and Bernard, Thanks for another surprising perspector! In Hyacinthos message #10184, Bernard Gibert ... I think that the perspector of the...
Dear Antreas, ... Good idea... but unfortunately, zooming in on my dynamic geometry sketch shows that they are not exactly concurrent... Friendly, Darij...
Hello I am working on the following problem: Let ABC a triangle and P a point What is the locus of P so that lines through Incenter and Circumcenter of...
Dear Antreas, [APH]: Let ABC be a triangle, P a point, A', B', C' the orth. projections of H on AP, BP, CP, resp. and Ea, Eb, Ec the midpoints of AH, BH, CH...
Dear Paul ... Thank you. Nice quintic ! The reflection conjugate of P is also known as the ANTIGONAL of P? The original version of the problem I had composed...
Dear Darij ... Hmmmm...... Apo idees .... allo tipota!! [free translation: I am full of ideas!!] Here is another one (idea, I mean): What point is (where is...
... This version is better than the original one below, since we can compose variations, like these ones: (1) Let PaPbPc be the the pedal triangle of P, A',...
Prove or disprove that with the bisectors, heights, medians, symmedians of a triangle you can construct another triangle. Thank you very much. And thanks for...
Dear friends of Hyacinthos, Antrheas, Darij, Juan Carlos, Jean Pierre...: Let a triangle ABC, A'B'C' is the orthic triangle of triangle ABC, H the orthocenter...
[APH] ... http://forumgeom.fau.edu/FG2001volume1/FG200109index.html This question reminded me of an open problem in that cited paper from 3 years ago. Perhaps...
Dear Ricardo, ... Very nice problem, thanks! Here is my solution: At first, I will show that AE = AF. Indeed, consider the circumcenter O of triangle ABC. The...
I found a different (wrt those proposed at http://www.cut-the-knot.org/Curriculum/Geometry/Quadri.shtml#Treatise ) pure geometric way to prove the following: ...
Dear friends:_ From the solution of Darij, send a euclidea. Let a triangle ABC, A'B'C' is the orthic triangle of triangle ABC, H the orthocenter of ABC, the...
... Let's use the points E,F for locus problems: Let ABC be a triangle, P a point and A'B'C' the cevian (or pedal) triangle of P. The line B'C' intersects the...
Let ABC be a triangle, and P a point. Denote: (Reflection of BP in BC) /\ AC := Ab (Reflection of CP in BC) /\ AB := Ac Oab := The circumcenter of ABAb Oac :=...
Dear Antreas, ... C(O,R) + cevian lines of O + line X186-X523 ... your cubic is the isogonal transform of K044, the Euler central cubic. it contains O, H, X24,...
Let ABC be a triangle, P a point, and A'B'C' the cevian triangle of P. The perpendicular to AA' at A' intersects AB, AC at Ab, Ac, resp. The perpendicular to...
The orthic triangle of the medial triangle of ABC, and the circumceviam triangle of H, are perspective at some point on the Euler line of ABC. At which point? ...
Dear Antreas, [APH]: The orthic triangle of the medial triangle of ABC, ... *** This is X(631), dividing OG in the ratio 3:2. The two triangles are indeed...
Dear Antreas; you wrote ... The orthic triangle of the medial triangle of ABC, and the circumceviam triangle of H are homothetic with factor 4 Since O en H are...
Let ABC be a triangle, and A'B'C' the circumceviancevian triangle of H. Ab, Ac := The orth. projections of A' on BB', CC', resp. Bc, Ba := The orth....
... With Cabri, yes... Center is 33,2337464291 cm in Kimberling triangle, not is catalogued... ... yes, with Cabri... Center of perspective is 12,4818250323 cm...
... Dear Ricardo The questions are identical: The Circumcenters of the triangles A'AbAc, B'BcBa, C'CaCb are the vertices of the orthic triangle. APH --...
... Yes, with Cabri... the point is -1,5641974768, X(1112) in ETC of Kimberling site. Greetings.. ... ______________________________________________ Renovamos...
... PARAMETRIZATION: Let Pa, Pb, Pc be three points on the lines OaHa, ObHb, OcHc, resp [Euler lines of A'AbAc, B'BcBa, C'CaCb] such that: PaOa / OaHa = PbOb /...
... GENERALIZATION (LOCUS): Let ABC be a triangle, P a point, and A', B', C' the reflections of P in BC, CA, AB. Ab, Ac := The orth. projections of A' on PB',...
Dear Antreas and friends of Hyacinthos The triangle ABC has unit area. E, F and G are points on the sides BC, CA and AB, respectively, such that AE bisects BF...
