I started from the formulas for R^2, ra^2 and s in terms on a, b, c, namely R^2 = ((a^2 b^2 c^2)/((a + b - c) (a - b + c) (-a + b + c) (a + b + c))), ra^2 =...
Dear Hyacinthos friends, I want to draw a conic of the pencil generated by two known conics, knowing also its center. How can I get the five points needed? ...
Dear Quim, ... the center must lie on the nine points conic of the pencil to get a solution. this conic passes through the two centers of the two conics and ...
Quim The two conics intersect in 4 pts. Choose any other point in the plane to give the 5th point of another conic of the pencil. It's a slightly different...
Dear friends, let H be the orthocenter (intersection point of altitudes AH1, BH2, CH3), and and G be the centroid (intersection point of medians AM1, BM2,...
Dear Yakub, your point is not in the ETC Its barycentric coordinates are ((a^6+a^4(b^2+c^2) -5a^2(b^-c^2)^2 +3(b^2+c^2)(b^2-c^2)^2)/(b^2+c^2-a^2).... It also...
Dear Yakub, This result can be extended. Consider P=p:q:r (barycentrics, not on the sidelines) instead of H. (1) we have A1 = [0:p+q:r], A2 = [0:q:p+r] etc ...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2009volume9/FG200926index.html The editors Forum...
ForumGeom
ForumGeom@...
Nov 2, 2009 3:30 pm
18423
Dear friends, Some complements to my previous message. ... In fact we have : Points P and Y are ever aligned with G. Define K = Sum_6 (p^2q) = st-3u where...
... The following can all be expressed in terms of R, s, r_a tan(A/2) = r / (s-a) = r_a / s sin(A) = 2 sin(A/2) cos(A/2) = 2 t / (t^2+1), where t=tan(A/2) a =...
Currently the points X3083 and X3084 appear en ETC as X(3083) = INTERSECTION OF LINES X(1)X(2) AND X(37)X(494) X(3084) = INTERSECTION OF LINES X(1)X(2) AND...
No, but he says that M has trilinears (2R/a+1: 2R/b+1:2R/c+1). Is easy to prove from the definition that BMa:MaC=c/(2R)+1):(b/(2R)+1 or BMa:MaC=c+2R:b+2R and...
Dear Hyacintists, von Emmerich has wrtitten a book on the Brocard's Geometry. Does anyone have an electronic copy of this book or where can I access to it on...
Dear Hyacinthists and Jean Louis, I suppose the book is the following: A. Emmerich, "Die Brocardschen Gebilde und ihre Beziehungen zu den verwandten...
Dear Barry, I want obtain a relation ab+bc+ca in function only "s, R and r_a". Sir Francisco Javier send me a relation ab + bc + ca = (s^6 + (4 R ra +...
Jean Louis You may not be able to access the PDF from the internet archive You can get it from the open library http://openlibrary.org John S [Non-text...
Dear Catalin, ... Barry sent you the following: If t = tan(A/2) = ra/s then a = 2.R.sinA = 4.R.t/(1 + t^2) = 4.R.s.ra/(s^2 + ra^2) (1) bc = (abc)/a = 2.R.S/a...
Dear Friends, I'm looking for the book Synthetische Beweise Planimetrischer Sätze – Autor: Wilhelm Fuhrmann. I wish this book was sent to me, in pdf, via...
Dear friends Eric and Pierre, Please, inform me. 1. how you get this barycentric coordinates? 2. what do you think is it possible, using these coordinates, to...
Of course barycentrics give proofs of theorem, although synthetic proofs are better for all of us. I this case it is convenient the use of computer algebra to...
Dear Hyacinthos I send a file in french with conway notations expleting the mode of calculus The name of the file is "New point on Euler Line" Amically Michel...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the Hyacinthos group. File : /New point...
Hyacinthos@yahoogroup...
Nov 7, 2009 8:32 am
18440
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the Hyacinthos group. File :...
Hyacinthos@yahoogroup...
Nov 7, 2009 9:10 am
18441
I also have sent my calculations, with Mathematica and my package baricentricas.nb I have included the proof of the relation GP:PH = (2-1/(cosA cosB cosC))/3 ...
Dear Yakub, 1 --> when using P= p:q:r instead of barycentrics of H, everything turns easier (and a generalization --using a nine-points conic-- is obtained as...
Dear Yakub, Do you have a simple proof for this problem? (I have an algebraic proof not simple, and no other information) Best regards Nikos Dergiades ... ...
Dear Nikos Dergiades, yes I have a pure geometric proof which is similar to the solution of the problem in the problems section of journal Math. in School...
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