Let ABC be a triangle and P a point on its plane. We construct [the how, and the number of solutions is another story !] three similar triangles PAbAc, PBaBc,...
Let ABC be a triangle and A'B'C' the pedal triangle of a point P. Let A",B",C" be the traces of the bisectors of the angles B'PC', C'PA', A'PB' on B'C', C'A',...
1946
Jim Parish
jparish@...
Dec 2, 2000 11:05 pm
... <snip> ... Here is an alternative proof. Fact: Let ABC be a triangle, and P a point not on any sideline of ABC. Let A', B', C' be the traces of the...
1947
yiu@...
Dec 3, 2000 1:22 am
Dear Antreas, [APH]: Let ABC be a triangle and A'B'C' the pedal triangle of a point P. Let A",B",C" be the traces of the bisectors of the angles B'PC', C'PA', ...
1948
xpolakis@...
Dec 3, 2000 8:27 am
Dear Paul, ... The proof I sent can be shortened as follows: A /\ / \ / \ / \ C' \ / A" B' / \ / Q P \ / B"...
1949
xpolakis@...
Dec 3, 2000 8:46 am
Let P be a point on the plane of ABC. A /\ / \ / Ba Ca \ / \ / \ / \ Cb P Bc / \ /...
1950
Bernard Gibert
b.gibert@...
Dec 3, 2000 10:07 am
Dear Paul and friends, ... I wrote ... It's not difficult to show that the trilinear circumconic of a point P is a rectangular hyperbola iff P is on the orthic...
1951
Bernard Gibert
b.gibert@...
Dec 3, 2000 10:07 am
Dear all, ... [Paul] ... This cubic has been identified by Jean-Pierre and I think it's a really nice one because of its symmetry about the Spieker point Sp...
1952
xpolakis@...
Dec 3, 2000 11:35 am
Let (G1),(G2),(G3) be three congruent circles of radius t inscribed in the angles A,B,C of a triangle ABC. Which is the locus of their radical center as t...
1953
xpolakis@...
Dec 3, 2000 12:27 pm
Dear Paul, Following I am correcting the generalization: ... PA" PB" ... PC" ... Antreas...
1954
Atul Dixit
atul_dixie@...
Dec 3, 2000 4:34 pm
Respected Sir, Once Antreas Hatzipolakis had written in this group about a problem by Vaclav Koneveny which is as follows:- let C(I) be circle with center...
1955
xpolakis@...
Dec 3, 2000 5:55 pm
... The general theorem by Lemoine is this: Let PaPbPc be the pedal triangle of a point P. Take three points A',B',C' on the lines APa,BPb,CPc respectively,...
1956
xpolakis@...
Dec 3, 2000 7:54 pm
... ^^^^^^^^^^^ .... and someone may naturally wonder: How about if P = O?!! I think that the hyperbola is the isogonal conjugate of the line OgP (where gP =...
1957
yiu@...
Dec 3, 2000 11:20 pm
Dear Antreas, ... I think this locus is the OI-line. Best regards Sincerely, Paul...
1958
yiu@...
Dec 4, 2000 12:37 am
Dear Antreas, [APH]: Let P be a point on the plane of ABC. A /\ / \ / Ba Ca \ / \ / \ / \ Cb P Bc /...
1959
yiu@...
Dec 4, 2000 12:40 am
Dear Antreas, [APH]: Let P be a point on the plane of ABC. A /\ / \ / Ba Ca \ / \ / \ / \ Cb P Bc /...
1960
Bernard Gibert
b.gibert@...
Dec 4, 2000 5:44 am
Dear all, ... ^^^^^^ please read X65, P, Na ceva P are colinear. Sorry. Best regards Bernard...
1961
xpolakis@...
Dec 4, 2000 2:13 pm
Dear Paul ... ^^^^^^^^^^^ I am afraid that for your, and any other computer in FLORIDA, will be too difficult even the system of equations we get if we replace...
1962
xpolakis@...
Dec 4, 2000 2:17 pm
Dear Paul, ... In my opinion, the Darboux cubic is in Triangle cubics what is the circumcircle in Triangle circles! Such basic! Probably the followwing...
1963
xpolakis@...
Dec 4, 2000 7:03 pm
... No, at least to me. So, next time I see it posted, I will refer to Alex Bogomolny's Inequality :-) Let's prove it: In cyclical form reads: ...
1964
xpolakis@...
Dec 4, 2000 8:51 pm
Probleme de Darboux: On considere les coniques circonscrites a un triangle telles que les normales aux trois sommets du triangle soient concourantes en un ...
1965
yiu@...
Dec 4, 2000 9:09 pm
Dear Antreas, [APH]: Let P be a point on the plane of ABC. The perpendicular to AP at P intersects AC,AB at Bc, Cb, respectively. BP AB,BC...
1966
Fred Lang
fred.lang@...
Dec 4, 2000 9:34 pm
Dear Hyacinthers, In Mathematical Magazine 1937, I have read the following paper of J.H.Weaver: "Describe the set of points P such that the cevian triangle of...
1967
Paul Yiu
yiu@...
Dec 4, 2000 10:15 pm
Dear friends, Communications with Atul Dixit and Antreas lead to the following observation: Let P be a point with traces A_P, B_P, C_P. Denote by L1 the line...
1968
xpolakis@...
Dec 4, 2000 10:41 pm
On 2 and 3 Nov 1999 Clark Kimberling had posted the following to geometry-college: ... Antreas...
1969
yiu@...
Dec 4, 2000 10:43 pm
Dear friends, [PY]:Let P be a point with traces A_P, B_P, C_P. Denote by L1 the line joining the perpendicular feet of A_P on the > cevians BB_P and CC_P. Let...
1970
Alexander Bogomolny
alexb@...
Dec 5, 2000 2:43 am
Antreas Hatzipolakis wrote ... Alas, I shall have to work harder to have my name survive my allotted time. I got this inequality about 4 years ago from Ania...
1971
Jean-Pierre.EHRMANN
jean-pierre.ehrmann@...
Dec 5, 2000 5:04 pm
Dear Antreas and other Hyacinthists, ... A funny problem. Of course the locus of P is the Darboux cubic and the locus of the center M(p,q,r) should be the...
1972
xpolakis@...
Dec 5, 2000 8:04 pm
The problem on the subject was posted by Frans Gremmen to geometry-college. See: http://forum.swarthmore.edu/epigone/geometry-college/shalshiquul (Frans wants...
