Dear all, Another variation: Let P be a point, A'B'C' its (Cevian) traces. Let Ab and Ac be the orthogonal projections from A' to sides b and c respectively. ...
Dear all, In addition to Antreas' orthiac and synorthiac triangles we can also define pediac and synpediac triangles: Let P be a point, A'B'C' its pedal...
Have we already discussed the combination on the subject line? That is, which is the locus of P such that: P, its isog. conj. P*, and the centroid of its pedal...
Dear Floor and Jean-Pierre, ... Another interesting appearance of McCay in circumcevians! In an other problem (by Paul) we have seen that the McCay cubic is...
Dear Jean-Pierre, I was wondering what a generalization of the Orthiac/Synorthiac triangles would be. I think that we can generalize them analogously to the...
Dear Jean-Pierre, [ND]>> Sorry for my ignorance. ... [JPE]>You mean your cleverness, I think. Thank you very much. But what I wrote is true. I feel as...
Dear Jean-Pierre, ... ..... and I thought that no cubic appears in this configuration! :-) Very Interesting! I have to study it carefully. So far we have seen...
Dear all, Let P be a point, gP its isogonal conjugate. Let A'B'C' and A"B"C" be their circumcevian triangles respectively. It is easy to see that the lines...
Dear Jean-Pierre, As you remarked, "It is very late now in France and in Greece" and probably it is better to sleep than to compose conjectures! Anyway, I make...
Dear Jean-Pierre, ... Or, in a more technical language: The centroids G'a, G'b, G'c of the Orthiac triangles A'AbAc, B'BcBa, C'CaCb form a triangle G'aG'bG'c...
Dear Hyacinthians, Non-degenerate cases of Neuberg's cubic have the incenter I on the oval, and we know that any line (not parallel to the asymptote) through I...
Dear Jean-Pierre, ... I think that these two groups of triangles are very interesting! Let's name them temporarily (or not!) as: Triangles A'AbAc, B'BcBa,...
Dear Jean-Pierre, ... So, we have the Theorem: Let AA', BB', CC' be the three altitudes of ABC, and Let Ab, Ac be the orth. proj. of A' on AB, AC resp. Bc, Ba...
... Dear Bernard, First, Thank You for your reply! Another recent conjecture of mine is this (which, I hope isn't false!): Let ABC be a triangle, and A'B'C'...
Dear Jean-Pierre, [APH] ... Hmmm... If one tries it analyticaly, he has to work a week, I am afraid! Let P = (x:y:z) in normals. 1st step: Computation of the...
Dear Antreas, ... directrix, ... is the ... circumcenter. ... such that ... 2ang(BB'O). ... ______________ There is a trigonometric solution but I don't like...
Let ABC be a triangle and Gp the centroid of the pedal triangle of P. Which is the locus of P such that the line PGp is parallel to the Euler line of ABC? APH...
Dear Paul, [ND]; ... [PY] ... ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Which is what I should have written! (in the phrase: "A2B2C2 the medial...
... Dear Fred, I like these results [M is almost everywhere!], and thank you! Now, next steps could also be: Add one more member in the set {P,P*,O,O1,O2}, ...
Nikolaos Dergiades asked (wording mine): Let ABC be a triangle, A1B1C1 its medial triangle, and A2B2C2 the medial triangle of the cevian triangle of P. For...
Dear all, Is there a point P? such that: ABC is a triangle and A1B1C1 is its median triangle, A2B2C2 is the median triangle of the cevian triangle of P...
Dear Paul, ... Dear Paul, Two such hyperbolae solve an old problem of mine: To construct a triangle if are given A, b + R, c + R. Analysis: Let ABC be the...
Dear all, We know that the Lucas cubic is the locus of P for which the Cevian triangle is orthologue to ABC. Which is the locus of P for which the PreCevian...
Dear Hyacintos! Let Z is inside triangle ABC, and A A1,B B1,C C1 are the chevians passing trough Z. S1 is area of A B1 C1 triangle, and S2, S3 we define in the...
It seems to me that by analogy to: ... where the locus of P is McCay + Something else, and where O is the pivot of McCay, one may conjecture: Let G1 and G2 be...
Dear friends, Is it true that: if three internal bisectors of a triangle equal to bisectors of another triangle then these triangles are equal? Best regards ...
