Dear Antreas, ... ^ This should be Pa. Your condition is easily seen to be equivalent to the condition that the B-parallelian and the C-parallelian through Pa...
8782
Antreas P. Hatzipolakis
xpolakis
Dec 6, 2003 10:15 pm
Let ABC be a triangle and Pa a point. The parallel to AB through Pa intersects BC at Aab The parallel to AC through Pa intersects BC at Aac Let A'ab, A'ac be...
8781
Antreas P. Hatzipolakis
xpolakis
Dec 6, 2003 7:09 pm
Is there a triangle whose the altitudes AA', BB', CC' are bisected by the orthocenter H? (ie AH = HA' and BH = HB' and CH = HC') In general: Let ABC be a...
8780
Darij Grinberg
darij_grinberg
Dec 6, 2003 6:44 pm
Dear all, I have finished my paper "Generalization of the Feuerbach point". It has 44 pages; for the first two Fontene theorems, the first 10 pages are enough....
8779
George Baloglou
baloglou@...
Dec 6, 2003 6:32 am
... Since Andreas -- to whom I recently sent a copy of my philological book cited above in appreciation of long-term correspondence -- has revived (or rather...
8777
Antreas P. Hatzipolakis
xpolakis
Dec 5, 2003 10:44 pm
... Similarly B*,C*. Are the triangles ABC, A*B*C* perspective for P = some simple point (H,O,I, ....) ? Antreas --...
8776
Antreas P. Hatzipolakis
xpolakis
Dec 5, 2003 10:28 pm
Dear Nikos Thanks for the solution and Best Wishes for your nameday (6/12) Greetings Andreas --...
8775
Nikolaos Dergiades
ndergiades
Dec 5, 2003 9:59 pm
Dear Antreas, Let angle BAA' = 2x, angle CAA' = 2y. On the bisector (b1) of angle BAA' we take an arbitrary point K' and let K'' be the reflection of K' in...
8774
Darij Grinberg
darij_grinberg
Dec 5, 2003 9:38 pm
Dear Sergei Markelov and all who may be interested, I have uploaded a short note named "Anti-Steiner points with respect to a triangle" on my website; this...
8773
Antreas P. Hatzipolakis
xpolakis
Dec 5, 2003 8:24 pm
Let ABC be a triangle and AA' a given cevian. To construct three CONGRUENT circles (K), (L), (M) such that: (K) is inscribed in angle(BAA') (ie touches AB,...
8771
Steve Gray
thimq
Dec 5, 2003 5:46 am
The generalization found by Michael deV which you refer to is a special case of something still more general that I found a few years ago. You may wish to...
8770
Eisso Atzema
atzema@...
Dec 4, 2003 9:01 pm
Fellow Geometers, As some of you might know, I am working on a bibliography of known properties of quadrilaterals. This is a long term project that will mostly...
8769
Antreas P. Hatzipolakis
xpolakis
Dec 4, 2003 5:04 pm
Let ABC be a triangle, P a point and PaPbPc its pedal triangle. The parallel La to BC through P, intersects AB at Lab and AC at Lac. Let A' be the reflection...
8768
jpehrmfr
Dec 4, 2003 4:20 pm
Dear Hyacinthists, I wrote ... I wanted to write UVW and PaPbPc are directly similar. I apologize for the typo. Jean-Pierre...
8767
jpehrmfr
Dec 4, 2003 3:59 pm
Dear Darij [JPE] ... [DG] ... I just use the properties of the Miquel point : UVW is a tringle indcribed in ABC; P (Miquel point) is the common point of the...
8766
Darij Grinberg
darij_grinberg
Dec 4, 2003 3:34 pm
Dear Jean-Pierre Ehrmann, Thank you very much for the proofs using pivot point theory. I will add some remarks. ... I don't understand how you draw the last...
8765
Alexey.A.Zaslavsky
zasl@...
Dec 4, 2003 5:53 am
Dear Darij! ... (7) can be proved without using (1)-(6). If the conic is a circle it follows from Ceva theorem and other cases are projectively equivalent. Now...
8764
Eric Danneels
efn4900
Dec 3, 2003 9:14 pm
Dear Hyacinthians, message 7504 led to some results on orthopoles. In message 7550 I made the following statement: (rephrased) Consider a triangle ABC with H =...
8763
Antreas P. Hatzipolakis
xpolakis
Dec 3, 2003 7:18 pm
Dear Jean - Pierre ... In other words: Let Ma be *the* point on the line segment BC such that: MaB + MaMab = MaC + MaMac where Mab, Mac are the orthogonal...
8762
jpehrmfr
Dec 3, 2003 5:56 pm
Dear Darij ... Here are some quick elements of answer : As <BA''C = -phi-<BAC+phi = -<BAC mod Pi, A'' lies on the circle BCH. It follows that the Miquel point...
8761
Darij Grinberg
darij_grinberg
Dec 3, 2003 1:43 pm
Given a triangle ABC and an angle phi (directed angle modulo 180), we construct the lines through A, B, C which make the angle phi with the lines BC, CA, AB,...
8760
Paul Yiu
yiuatfauedu
Dec 2, 2003 11:34 pm
... [PY]: Thank you very much. Earlier today I was preparing my number theory notes ... Of course I have not read it carefully. It was discovered 2 weeks ago. ...
8759
Paul Yiu
yiuatfauedu
Dec 2, 2003 11:25 pm
Dear Antreas, Thank you very much. Earlier today I was preparing my number theory notes for the coming semester, and was checking the record of Mersenne...
8758
Antreas P. Hatzipolakis
xpolakis
Dec 2, 2003 10:45 pm
... Quoting the first two paragraphs of the web page: ORLANDO, Florida - December 2, 2003 -- Michael Shafer, a 26 year-old volunteer in the Mersenne.org...
8757
Antreas P. Hatzipolakis
xpolakis
Dec 2, 2003 10:25 pm
Dear Jean-Pierre ... You mean Lemoine (as in the subject line) ... The perpendicular to BC at Ma intersects AB at Ab, and AC at Ac. Define A' = BAc /\ CAb....
8756
Paul Yiu
yiuatfauedu
Dec 2, 2003 2:08 pm
Dear Antreas, [APH]: In triangle ABC, let P, P* be two isogonal conjugate points, Pa,Pb,Pc the midpoints of PA,PB,PC, resp., and Ma,Mb,Mc the midpoints of...
8755
Antreas P. Hatzipolakis
xpolakis
Dec 1, 2003 10:56 pm
In triangle ABC, let P, P* be two isogonal conjugate points, Pa,Pb,Pc the midpoints of PA,PB,PC, resp., and Ma,Mb,Mc the midpoints of P*Pa, P*Pb, P*Pc, resp. ...
8754
Antreas P. Hatzipolakis
xpolakis
Dec 1, 2003 8:41 pm
A new book, co-authored by the friend and listmember George Baloglou (Associate Professor of Mathematics at the State University of New York, Oswego) An...
8753
Antreas P. Hatzipolakis
xpolakis
Dec 1, 2003 8:07 pm
... Rephrasing it: Let A1A2A3.... An be a regular polygon whose angle(A3A1A6) = 15 deg. How many diagonals equal to A1A6 has it? Let w be the angle that a side...
8752
jpehrmfr
Dec 1, 2003 4:56 pm
Dear Hyacinthists looking at the beginning of the very interesting from EH Lemoyne : Suite de theoremes et de resultats concernant la geometrie du triangle ...
