Dear Alexey Thank you for your remarks. I will try to draw all the envelope with Cabri and maybe SketchPad if possible. Friendly Francois ... [Non-text...
Hello, everyone. I am Mahathey from India.I joined the group recently.I wanted to share a problem with you people.It is: There are n given circles in a plane[...
Dear Francisco and Eric, Thank you very much for your messages! I am very happy to receive your messages. I would like to thank Peter J.C. Moses for remark...
Dear Quang, I would like to present the following generalization: Let PaPbPc be the cevian triangle of P wrt triangle ABC A', B', C' are reflections of A, B, C...
Dear Eric, Thank you for interesting generalization. If I am not wrong, if barycentrics of P = (p : q : r) then results are: Two triangles ABC and A''B''C''...
Dear Eric and All My Friends, We can also take one more point and get one cubic locus. Detail as following: Barycentrics of P = (p : q : r), X = (x : y : z)....
Dear Mahathey, I think that the solution to this problem is for every combination of 3 circles C1, C2, C3 of the n circles to construct the circle C that is...
Dear Alexey, and Francois This is very interesting. If the points P, Q are on the sides of angle A in order to have (AP+AQ)/(APQ) = (AB+BC+CD+DA)/(ABCD) =...
Dear Tuan, [snip] ... this is the pivotal cubic with pivot taaP and isopivot P (tX = isotomic conj. of X, aX = anticomplement of X) thus, C(X3) = pK(X1073,...
Dear Nikolaos Dergiades, It is worthwhile to discuss whether such a circle is unique. At this point, I have difficulty:Is it really easy or elementary to prove...
Dear Nikos! Thank you for interesting message. But are you sure that first conic touches the lines C'D, CD' and not AB', A'B? This is correct if the points P,...
Alexey.A.Zaslavsky
zasl@...
Mar 5, 2008 9:36 pm
16183
Dear Hyacinthists, ... [...] ... I was able to construct a triangle XYZ where XY=h_b, XZ=h_a and Z-Y=A-B. But... shouldn't I show that X=C? I see that if I...
Dear Alexey, you are right. The first conic touches also the lines AB', A'B. I didn't mentioned it because their tangency points have not to do with the true...
Dear Nikos! It seems that I understood which is the set of our lines. Firstly I want note sime properties of your quadrilateral A'B'C'D'. These properties are ...
Alexey.A.Zaslavsky
zasl@...
Mar 6, 2008 1:16 pm
16186
Dear Mahathey, my conclusion for the tangency to 3 circles is not correct. It is possible the required circle to be tangent only to two of the n circles. It is...
Dear Mahathey and Nikolaos ... The uniqueness is clear : suppose that two distinct congruent circles surround our n circles; if these two circles intersect at...
Dear Jean-Pierre Very good proof for the uniqueness! How do you mean the iterative construction of the minimal circle e.g. if we have 3 circles (A,r1), (B,r2),...
Dear Nikolaos ... I suggest the following (but it is just a conjecture), starting with n circles (O[k], r[k]) (none of them inside another one) For 1<=i<j<=n,...
Dear Nikos! must be written as ... No, if B', D' are in the same semiplane that B then we have the lines passing only through B' and not D'. So if the point P...
Alexey.A.Zaslavsky
zasl@...
Mar 7, 2008 2:46 pm
16192
Dear Alexey, I can't understand it. Perhaps we have different figures. In my figure if S1 is the intersection of AD, BC and S2 is the intersection of AB, CD...
Dear Hyacinthos In a recent discussion, I note that names of point are not very clear I propose another notation: Point on (BC) have name Ax, on (AC) Bx, on...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2008volume8/FG200807index.html The editors Forum...
ForumGeom
ForumGeom@...
Mar 10, 2008 3:03 pm
16195
Dear Nikos I can't understand it. Perhaps we have different figures. In my figure if S1 is the intersection of AD, BC and S2 is the intersection of AB, CD then...
Alexey.A.Zaslavsky
zasl@...
Mar 11, 2008 1:46 pm
16196
Dear Hyacinthers, a have put a new file in the list: "PedalCircleCenterTransformation". it is a study of the transformation that associate to a point P, the...
Dear Hyacinthians, as I was playing with some Cevian triangles I noticed the following: I) Let A'B'C' be the Cevian triangle of a point P w.r.t. a triangle ...
Dear Eisso Very nice configuration It seems to me that V.Thbault has something to do with it but I don't remember where. As for your drawing, maybe there is...
Dear Eisso, ... this is the Orion transform in Clark's ETC. See also the thread : Another stellar (or flowered) transformation, Hyacinthos #7999 & sq. The...
