Dear Bernard! ... My proof isn't purely synthetic, but the calculations are minimal. We know that the inversion wrt the circumcicle of X(15) is X(16) and this...
Alexey.A.Zaslavsky
zasl@...
Apr 4, 2005 5:03 am
11149
Hi everybody, I am new in this group and this is my first message. I hope the following problem is not boring for you! I have read somewehere that the tangent...
Hello dear members of this group: This problem was proposed in some OIM. I wish to find the solution. "Find the locus of the middle points from the chords of...
... My calculations give: (a^2 + b^2)*(b^2*X^2 + a^2*Y^2)^2 == a^2*b^2*(b^4*X^2 + a^4*Y^2) What's the name of this curve? Best regards, Francisco Javier...
Dear Bernard! ... I found general fact. Let the Apollonius points X(15), X(16) of triangles ABC and XYZ coincide. Then the pedal triangles of X, Y, Z wrt ABC...
Alexey.A.Zaslavsky
zasl@...
Apr 7, 2005 10:18 am
11154
Dear Hyacinthians, Has this been noted before? Let A'B'C' be the orthic triangle, and A'' the orthocenter of AB'C', similarly B'' and C''. The triangles A'B'C'...
Dear Floor, [FvL]: Let A'B'C' be the orthic triangle, and A'' the orthocenter of AB'C', ... *** These two triangles are indeed oppositely congruent. The...
Dear Floor, I can't tell if this has been noted before but I can add that: - triangles A'B'C' and A''B''C'' are identical; - the homothetic center is X(389)...
Dear Eric and Floor, [FvL]: Let A'B'C' be the orthic triangle, and A'' the orthocenter of AB'C', similarly B'' and C''. The triangles A'B'C' and A''B''C'' are ...
Dear Bernard and Alexey In general, what can be said about triangles having the same isodynamic points? Particularly what can be said about triangles having...
Dear Alexey I guess the following results I checked with Cabri: 1° There are infinitely many triangles ABC inscribed in a circle {Gamma} having W and W' as...
Dear friends It is easy to construct the family of triangles ABC inscribed in a circle {Gamma} having the (inverse) points W and W' as isodynamic points...
Dear friends I am always obsessive by the family of triangles ABC inscribed in a circle {Gamma} and having the same Lemoine point L. I search a simple...
Dear friends Finally, I find the following formula: 3.r^2 = R^2 - d^2 linking R the radius of the ABC-circumcircle noted {Gamma}, d = OL the distance beetween...
Dear Paris Thank you for your swift reply. Now I understand why I became a Hyacinthos addict. I will look at your paper with great interest. Friendly François...
Dear Quim and Paris and Hyacinthos friends I just get a look at F.G-M book 2442 (Theorem1059) page 1222. I read it very carefully for a long time but sorry,...
Dear friends In fact, this Cabri's theorem on cross-ratios is not a theorem on Lemoine point but a projective theorem on conics in a projective plane. So ABC...
Dear friends I think we have the following proof: We choose an affine structure on the projective plane so that the tripolar line of L wrt ABC is the line of...
Dear friends In the end, I get the following construction of D on the line ALA': We construct the symmetric a' of A wrt O the center of {Gamma} and the ...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200508index.html The editors Forum...
ForumGeom
ForumGeom@...
Apr 11, 2005 9:27 pm
11172
Dear Francois, you wrote ... I'm not a specialist in projective geometry so I send you this message to see if my reasoning is correct A circumconic of a...
Dear Eric (and dear Paris) That's OK for me. I made a similar reasoning choosing an affine structure on the plane by taking the polar line of L wrt the...
Dear friends I saw another reason to rejoice about the configuration of the F-family of triangles sharing the same circumcircle Gamma and the same Lemoine...
Dear Francois! The problem is the following: Given A on {Gamma}, construct simply B and C on {Gamma} so that L is the Lemoine point of ABC. F.G-M proof is...
Alexey.A.Zaslavsky
zasl@...
Apr 13, 2005 5:04 am
11176
Dear friends I send you 3 Cabri-drawings on the Lemoine configuration seen in an hyperbolic framework. 1° The first Lemoine-Poincaré.fig: a picture seen in...
Dear Francois, ... I think you'll have to place your drawings in the "Files" section of the Hyacinthos group because attachments and graphics are not allowed ...
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