Dear All My Friends, From incenter I we construct one line perpendicular to sidelines BC. This line cuts AB at Ab, cuts AC at Ac and cuts incircle (other than...
14419
Francois Rideau
francoisrideau
Nov 8, 2006 5:01 am
Dear friends ... Sorry, the map f is not involutive, ( I was mistaken with another configuration!), but the fixed points of the map f are well the foci of ...
14420
Quang Tuan Bui
bqtuan1962
Nov 8, 2006 6:26 pm
Dear All My Friends, By calculations I have found: - Triangle AiBiCi has barycentrics: Ai = (a^2 : sa*sb : sa*sc) Bi = (sb*sa : b^2 : sb*sc) Ci = (sc*sa :...
14421
?????????
tl_em@...
Nov 8, 2006 11:42 pm
Dear Tuan, ... This line cuts AB at Ab, cuts AC at Ac and cuts incircle (other than touch point with BC) at Ai. Similarly we construct Bc, Ba, Bi, and Ca, Cb,...
14422
Quang Tuan Bui
bqtuan1962
Nov 9, 2006 6:03 pm
Dear All My Friends We can generalize the circumconic (Co) as follow: Suppose I is any point P with barycentrics (p : q : r). Construct A1B1C1 as before. Six...
14423
Emelyanov
tl_em@...
Nov 9, 2006 10:47 pm
Dear Tuan, I found many interesting facts about the Nagel point. For example: let A'B'C' be the cevian triangle of Nagel point, then 1) we always can constract...
14424
Quang Tuan Bui
bqtuan1962
Nov 10, 2006 2:31 am
Dear Lev, Thank you very much for your proof in previous message and interesting results in this message. Also thank you for the information I need which you...
14425
Quang Tuan Bui
bqtuan1962
Nov 10, 2006 4:17 am
Dear All My Friends, If we choose P as circumcenter then we have one very simple circumconic: - The barycentrics equation: a^4*y*z + b^4*z*x + c^4*x*y = 0 -...
14426
Quang Tuan Bui
bqtuan1962
Nov 10, 2006 6:15 am
Dear All My Friends, The general circumconic (Co) (with any point P) has one interesting feature: Let Q is perspector of (Co), gQ is isogonal conjugate of Q,...
14427
Quang Tuan Bui
bqtuan1962
Nov 10, 2006 8:41 am
Dear All My Friends, I am very sorry. The features related with perspector Q, gQ, tgQ, X, X' of one conic and operation barycentric product are true for any...
14428
Francois Rideau
francoisrideau
Nov 10, 2006 8:51 am
... [Non-text portions of this message have been removed]...
14429
Jeff Brooks
jbrooks_tulsa
Nov 10, 2006 9:33 am
Hey François, I'll definitely look closer at your description below. How might we relate (if at all possible) these relationships to orthogonal polynomials...
14430
Francois Rideau
francoisrideau
Nov 10, 2006 10:17 am
Dear Jeff Good to remember me the name of this great russian man. Maybe there is a connection with linkages? Friendly François [Non-text portions of this...
14431
Jeff Brooks
jbrooks_tulsa
Nov 10, 2006 10:47 am
Well, besides mine, there are only three other references to him in the Group. But, it's possible I did not apply the correct filter. :-) Sincerely, Jeff...
14432
Francois Rideau
francoisrideau
Nov 10, 2006 10:38 pm
Dear friends Given a triangle ABC, I give you other properties of the configuration of the family of the pedal triangles abc of points M on a line L in...
14433
Francois Rideau
francoisrideau
Nov 10, 2006 11:04 pm
Dear friends I forgot to tell you something in the last theorem 6 of my previous post: We know that the four lines L1, L2, L3, L4 bound 4 triangles which give...
14434
Francois Rideau
francoisrideau
Nov 11, 2006 8:03 am
Dear friends ... Sorry, my theorem 3 is wrong. My sight is not so good now and maybe I made a mistake using a Cabri macro. That's why I have had some...
14435
jpehrmfr
Nov 11, 2006 8:47 am
Dear Francois you wrote ... configuration of ... inversive ... the line ... Simson ... a'b'c', ... Here is another one : If the line L intersects BC, CA, AB at...
14436
Francois Rideau
francoisrideau
Nov 11, 2006 10:10 am
Dear Jean-Pierre Thanks for your drawing. Suddenly, it seems to me that triangles both perspective and directly similar have been already studied in the past...
14437
jpehrmfr
Nov 11, 2006 10:41 am
Dear Francois ... and ... remember it? You are probably right. The only thing that I know is that, when the similitude is not an homothecy, the perspector and...
14438
Quang Tuan Bui
bqtuan1962
Nov 11, 2006 3:49 pm
Dear All My Friends, Some properties of this circumconic: 1. P and reflection of P in circumcenter share one common (Co) conic 2. If P on circumcirle then...
14439
Quang Tuan Bui
bqtuan1962
Nov 11, 2006 5:23 pm
Dear All My Friends, Center of this locus circumconic passing through X(2966), X(112), X(1576), X(1415) with perspector X(184) has barycentrics: a^4*(a^8 + b^8...
14440
Milorad Stevanovic
yumarince
Nov 11, 2006 8:53 pm
Dear friends, Let P be a point and A1=PA /\ BC and P1 is harmonic conjugate to P wrt A and A1, and analogously for P2 and P3.Then P1,P2 and P3 are...
14441
Nikolaos Dergiades
ndergiades
Nov 11, 2006 10:21 pm
Dear Milorad, The triangle P1P2P3 is the anticevian triangle of P = (x : y : z) in barycentrics and the Miquel point of ABC wrt P1P2P3 is the point in...
14442
Francois Rideau
francoisrideau
Nov 12, 2006 9:53 am
Dear friends I come back again to the Atul-Darij paper http://forumgeom.fau.edu/FG2004volume4/FG200406.pdf ... use the Pappus theorem to prove alignment of...
14443
Quang Tuan Bui
bqtuan1962
Nov 12, 2006 11:21 am
Dear All My Friends, In the case P = incenter, three lines AA2, BB2, CC2 are concurrent at X(651). In general these three lines are not concurrent. By some...
14444
Francois Rideau
francoisrideau
Nov 12, 2006 5:13 pm
Dear friends And it fact it easy to prove equalities of crossratios. I keep notations of my previous post. For example, if A', B', C' , D' are the orthogonal...
14445
Quang Tuan Bui
bqtuan1962
Nov 13, 2006 2:47 pm
Dear All My Friends, Given triangle ABC; point P with barycentrics (p:q:r); point U with barycentrics (u:v:w). A perpendicular line from P to BC cuts AB at Ab,...
14446
ForumGeom
ForumGeom@...
Nov 13, 2006 4:09 pm
The following paper has been published. It can be viewed at http://forumgeom.fau.edu/FG2006volume6/FG200633index.html The editors Forum Geometricorum ...
14447
Quang Tuan Bui
bqtuan1962
Nov 14, 2006 8:46 am
Dear All My Friends, Today I search one point in ETC Search Table. Suddenly I see strange search value of X(519). Here it is: 14.03030303030 I try to calculate...
