... If DEF is the cevian triangle of P, then I think that the locus of P such that areas APE + BPF + CPD = APF + BPD + CPE is the quartic with barycentric...
... Dear Jean-Pierre Some quick generalizations: 1. min/max for P lying on a well-defined circumellipse. 2. ABCD := a quadrilateral inscribed in a circle. ...
Let ABC be a triangle, and P a point. Ac := The orthogonal Projection of C on AP Acc := The orthogonal Projection of Ac on AC Ab := The Ortogonal Projection of...
Dear colleagues! Let given a quadrilateral and two inscribed conics with focus U, U' and V, V'. Then the points UV^U'V" and U'V^UV' also are the focus of some...
Alexey.A.Zaslavsky
zasl@...
Jun 7, 2005 6:03 am
11303
Dear Alexey ... and V, ... inscribed conic. ... It is a nice result, though I suspect Bernard will give a reference. I do not know what proof you have in mind,...
Dear Alexey and Wilson [AZ] ... U' ... some ... [WS] ... reference. ... shown ... above ... all ... Perhaps, Bernard could say the following : If M->M* is a...
Dear Hyacinthians, I wonder if the following perspectivity is known Consider a triangle ABC and a point P Let A'B'C' be the circumcevian triangle of P wrt ABC ...
Dear Alexey, Wilson and Jean-Pierre, ... this is Special Isocubics 4.1.2. Best regards Bernard [Non-text portions of this message have been removed]...
Let ABC be a triangle, P a point and Lp := A'B'C' its trilinear polar (with A' on BC, B' on CA, and C' on AB) Let La, Lb, Lc be the parallels through P to...
Let ABC be a triangle, P a point and La, Lb, Lc the parallels through P to BC,CA,AB, resp. Ab := The 2nd intersection of the circle ABP and La Ac := The 2nd...
Dear Antreas ... The Mac Cay cubic ... They are allways perspective at the isogonal conjugate of P ... They are allways perspective at the complement of the...
Dear Jean-Pierre ... A way to generalize it is this: Let Q be a fixed point, and Lq := A'B'C' the trilinear polar of Q. Let P be a variable point and La, Lb,...
Dear friends: I have found the next curious relation: Be ABC acute triangle with H orthocenter and its excircles (I_a),(I_b) (I_c).If X,Y,Z are the midpoints...
... Denote F := UV /\ U'V' F' := U'V /\ UV' Now, if we consider the inconics with foci U,U' and F,F', then the points UF /\ U'F', U'F /\ UF' are just the...
Dear Juan Carlos ... (I_b) ... We have tXI_b = R|1-cos(B)+cos(C)| and tXI_c = R|1+cos(B)-cos(C)|; thus, if ABC is acutangle, tXI_b + tYI_c + tZI_a = tXI_c +...
Let ABC be a triangle, P a point A'B'C' the circumcevian tiangle of P, and A"B"C" the tangential triangle of ABC, A*B*C* the tangential triangle of A'B'C' I...
Let ABC be a triangle P a point, and La, Lb, Lc the parallels through P to BC,CA,AB, resp. Denote La /\ AB := Ab, La /\ AC := Ac Abb := The Reflection of P in...
Dear Antreas, ... this is pK(X3, X4) but I do not think it's correct. I find pK(X3, X193), a central pK with center K mentioned in Special Isocubics 3.2.4. ...
Dear Bernard ... [BG] ... Well... Let P = (x :y : z) be the actual trilinears of P We have PAb = zcscB, PAc = ycscC, and MaAb = AcP = ycscC, MaAc = AbP = zcscB...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/Index.html The editors Forum...
ForumGeom
ForumGeom@...
Jun 17, 2005 8:43 pm
11320
I have been unable to 'google' anything about Vecten the man, as opposed to geometric results named after him, other than that he was "a professor of...
dick tahta
dick@...
Jun 20, 2005 4:24 pm
11322
... This information comes from F.G.-M. The Vecten Theorem appeared in A.d.G. [=Annales de Gergonne] VII (1816-7), p. 321 ... aph --...
Tnanks Antreas for the reference. I assume the paper was by Vecten himself. But also that it would have been someone else who would have given, perhaps some...
dick tahta
dick@...
Jun 22, 2005 10:36 am
11324
... I had assumed that you would have seen this; "Ernst Wilhelm Grebe was the first to call the common point of ATa, BTb, and CTc the Vecten point. " from ...
Let ABC be a triangle, HaHbHc its orthic triangle, P a point and A'B'C' its cevian triangle Denote Ac := (Parallel from A to BHb ie Perp. to AC at A) /\ CC' Ab...
Dear friends, especially Keith Dean and Jean-Pierre Here are your posts No 4935 and No 4937 ... In last month, I have been working on problem of finding ...
[APH] ... that is, cotB + cot(B,C) ... cotC + cot(C,B) that is, ABC, A#B#C# are perspective. So we have the THEOREM Let ABC, A#B#C# be two triangles and P a...
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