Dear Alexei and Jean-Pierre another approach that needs an elementary construction is the following: but I can not give a synthetic proof. If X, Y are points...
I repeat to corredt my previous message Dear Alexei and Jean-Pierre another approach that needs an elementary construction is the following: but I can not give...
Dear Quang Tuan Bui and Jean-Pierre, ... point on ... Hmmm, difficult at first sight... Let F(P,U) be the singular focus of C(P,U). I have proven that F(P,U)...
Dear Jean-Pierre, Bernard and All My Friends, Thank you very much for your messages! I have some ideas which can help us in our investigations of these cubics....
Dear Hyacinthists, I don't know what happens/has hapenned but many messages related to this thread, including all mine, didn't show up on my inbox I will reply...
Construct (with R&C) the intersection of a line <r> with a conic (parabola) given by its focus <F> and directrix <d>. Dear Hyacinthists, Dear François, I will...
Dear Quang Tuan Bui and Jean-Pierre, ... Here is a construction of the singular focus F(U,P) of C(U,P) : Db = the reflection of the line BU in a bisector of...
Construct (with R&C) the intersection of a line <r> with a conic (parabola) given by its focus <F> and directrix <d>. Dear Hyacinthists, Dear François, I will...
Yes, nice solution and now I remember that I learned it more than fifty years ago. Of course the most important is the discussion which must follows on the ...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2007volume7/FG200716index.html The editors Forum...
ForumGeom
ForumGeom@...
Jul 2, 2007 7:21 pm
15359
Dear Hyacinthists, Dear François, It seems the messages are leaving/arriving normally again. I see now your solution is to draw a circle through two given...
Dear friends Given a conic <Gamma> in the plane, what can be said of an involutive transformation f of the plane such that points M and f(M) are always ...
Dear friends I give you an example of such an involutive map that I have found while doing some chowchows. I start with an equilateral triangle ABC with...
Dear All My Friends, Given triangle ABC and one point Pa on sideline BC. L is any line passing through vertex A. (Ob) = circumcircle of ABPa. (Oc) =...
Dear Tuan, ... If BPa.BC = m and if my calculations are correct then the locus of X is the cubic [ccyy+(bb+2m-aa-cc)yz-bbzz]x+2myyz+(2m-2aa)zzy = 0 in...
Dear friends. I see this property accidentaly on computer by Cabri. Given cyclic quadrilateral ABCD, AC intersects BD at I, let I1,I2,I3,I4 be incenters of...
Dear friends. I see this property accidentaly in computer by Cabri Given cyclic quadrilateral ABCD, AC intersects BD at I, let I1,I2,I3,I4 be incenters of...
Howard Eves writes that "The double interpretation of a pair of coordinates as either point coordinates or line coordinates and of a linear equation as either...
In acute triangle ABC,<A is less than 45 . Point D lies in the interior of triangle ABC such that BD=CD and <BDC=4<A. Point E is the reflection of B across...
Dear Jakob I still don't have a proof but I can add that incenters of ABC, BCD, CDA, DAB are on a rectangle ( see Morley, Inversive Geometry, for a proof); so ...
Dear Jakob You can also look at other in-excenters of your eight triangles, that is to say: 4 x 8 = 32 points and group them eight by eight on some well...
Dear Francois. You are right thank you, the excenters of those tringles also have that property, I draw and I see it seems the ellipses is similar, however I...
Let O be the circumcenter of ABC then the point D is the circumcenter of OBC. In order to prove that AD _|_ EF it is sufficient to prove that DF^2 - DE^2 =...
Dear My Friend, I prove one more general fact true for any triangle which you can use for your particular case: Given triangle ABC, O is circumcenter of ABC, D...
... Julian Lowell Coolidge, "A History of Geometrical Methods" has quite a few references to Pluecker (cf. his rather unusual index, p.440). A better source...
Ken Pledger
Ken.Pledger@...
Jul 23, 2007 3:18 pm
15375
Dear Francois, I am attempting to tackle this problem with a direct proof. But, my methods are long and laborious. It seems that the tangent line at <p> works...
Dear Jeff When you look at some isoconjugation (m <--> m') with 4 real fixed points, for example isotomic conjugation or isogonal conjugation, then m and m'...
Dear Jeff Of course, I don't know the answer! But in case of a circle, inversion have infinitely many fixed points when isoconjugation have only 4 fixed points...
