... Show ... Let BH,IF intersect at X; CH,IE intersect at Y The figure IXHY enclosed by parallels BH,IE and CH,IF is a parallelogram So HI bisects XY...(i) ...
9761
Eric Danneels
efn4900
May 4, 2004 6:16 pm
Dear Darij, in message 9725 you wrote about the antigonal conjugate: ... ... I think it is: The antigonal conjugate D' of D is the isogonal conjugate of the...
9762
Darij Grinberg
darij_grinberg
May 5, 2004 7:17 pm
Dear Eric, ... Oh yes, sorry. Thanks for the remark. By the way, the proof is easy: If D1 is the isogonal conjugate of D, then we can readily see that < BD1C =...
9764
Antreas P. Hatzipolakis
xpolakis
May 6, 2004 11:32 am
Let ABC be triangle whose BC is fixed and A moves on a given line L. What is the locus of its Incenter/excenters? In Particular: L // BC APH --...
9765
jpehrmfr
May 6, 2004 1:00 pm
... Suppose that your line L intersects BC at W. Your locus is a cubic through B,C,W; the three asymptots are the bisectors of (BC, L) and the perpendicular to...
9766
Gilles Boutte
g_bouttefr
May 6, 2004 2:27 pm
Dear Antreas, Let H_b (resp. H_c) be the pencil of couple of perpendicular lines (degenerate rectangular hyperbolas) through B (resp. C). Let D_b (resp D_c)...
9769
Darij Grinberg
darij_grinberg
May 6, 2004 7:57 pm
As some of you know, I participate in the German IMO training; this means I am one of the 16 students which are being prepared for a possible participation in...
9770
Alexey.A.Zaslavsky
zasl@...
May 7, 2004 9:03 am
Dear Darij and Barry! ... This problem can be reformulated. Let given two circles with centers O1, O2 and their two common tangents: external and internal. l1,...
9771
Darij Grinberg
darij_grinberg
May 8, 2004 4:13 pm
I see two very nice problems in the St. Petersburg Mathematics Olympiad 2002, Elimination Round: Problem 10/6 in an equivalent version ... The tangent to the...
9772
ben_goss_ro
May 8, 2004 10:36 pm
... I've only thought about 11/2, which seems to be the easiest one of these 3. By a quick angle chase we can show that the circle (IXY) passes through the S,...
9773
Darij Grinberg
darij_grinberg
May 9, 2004 10:20 am
Dear Grobber, In Hyacinthos message #9772, you wrote: [on 11/2] ... This is nice! Here is the proposed solution: The triangles AXI and AYI are congruent, since...
9774
rafinad2003
May 10, 2004 2:08 am
Dear Darij, ... ..... Here is the proposed solution: The triangles AXI and AYI are congruent, since AX = AY, AI = AI and < XAI = < YAI. Hence, XI = YI, and...
9775
rafinad2003
May 10, 2004 2:10 am
Dear Alexey and Darij, In msg 9770 Alexey wrote: ... This problem can be reformulated. Let given two circles with centers O1, O2 and their two common tangents:...
9776
Alexey.A.Zaslavsky
zasl@...
May 11, 2004 12:08 pm
Dear Darij! -> ... This is the partial case of next fact. Let given the triangle ABC and the point P. A', B', C' are the second common points of AP, BP, CP and...
9777
Alexey.A.Zaslavsky
zasl@...
May 11, 2004 1:03 pm
Dear Darij! ... After polar transformation we receive next proposition. Let I is the incenter of ABC, the line passing through I and parallel to AA' intersect...
9778
flatt000
May 11, 2004 7:44 pm
To generate a road in ray tracing, I need to get a section of cylinder when I just know the road width and the height in the midle (the edges are at 0). More...
9779
Gilles Boutte
g_bouttefr
May 11, 2004 9:02 pm
You wrote, on your site, by trigonometric evaluation : W = 2R sin(a) H = R [ 1 - cos(a) ] hence : R cos(a) = R - H In fact, you have rectangular triangle with...
9782
ForumGeom
ForumGeom@...
May 12, 2004 2:17 pm
The following paper has been published in FG. It can be viewed at http://forumgeom.fau.edu/FG2004volume4/FG200409index.html The editors Forum Geometricorum ...
9783
Peter Scales
peterjscales
May 12, 2004 3:19 pm
Dear flatt ? I could not access your site via the link you gave, but it doesn't matter as the follow up message from Gilles Boutte gave the essential...
9784
flatt000
May 12, 2004 5:42 pm
for your help. The solution is implemented and works fine. It is in fact finding the radius of the circle going through 3 points. It will be used for road and...
9785
Ken Pledger
Ken.Pledger@...
May 13, 2004 2:58 am
The following problem in Euclidean geometry was posted in other places by Gerry Wildenberg <gwildenb@...> but to no avail. I offered to forward...
9786
fvlamoenwxs
May 13, 2004 9:09 am
Dear all, With triangle ABC let D be the point in the plane of ABC such that AB^2 + CD^2 = AC^2 + BD^2 = AD^2 + BC^2. Which point is D? Kind regards, Floor....
9787
Alexey.A.Zaslavsky
zasl@...
May 13, 2004 9:28 am
Dear Floor! ... As AD^2-BD^2=AC^2-BC^2, CD is perpendicular to AB. So D is the orthocenter. Sincerely Alexey...
9788
jpehrmfr
May 13, 2004 9:30 am
Dear Floor ... The locus of M such as BM^2-CM^2 = BA^2-CA^2 is clearly the A- altitude. Thus D is (very) probably the orthocenter. Friendly. Jean-Pierre...
9789
Darij Grinberg
darij_grinberg
May 14, 2004 2:46 pm
Dear Rafi, ... [...] ... Sorry, I meant < XYI = < CXI. In fact, please read B for C and C for B throughout my proof. Sincerely, Darij Grinberg...
9790
Darij Grinberg
darij_grinberg
May 14, 2004 4:33 pm
Dear Hyacinthians, The following theorem is an example of a non-standard triangle geometry result because the proof (at least, the proof I know) uses a ...
9791
Darij Grinberg
darij_grinberg
May 16, 2004 9:35 am
In Hyacinthos message #3957, Paul showed an interesting fact about circumcevian triangles originating in a question of Antreas. I will restate this fact with...
9792
Darij Grinberg
darij_grinberg
May 16, 2004 9:50 am
My generalization of Chaogold's result in http://mathlinks.ro/viewtopic.php?t=5058 Let P be a point in the plane of a triangle ABC; an arbitrary conic k...
9793
Barry Wolk
wolkbarry
May 16, 2004 8:04 pm
... That result looks false to me. Start with distinct overlapping circles c1, c2 and c3, and define {X,X'} = c2 /\ c3, {Y, Y'} = c3 /\ c1, {Z, Z'} = c1 /\ c2....
9794
Gilles Boutte
g_bouttefr
May 16, 2004 9:31 pm
... Precisely, the three pairwise radical axis of the 3 circles , i.e. the sidelines of ABC, are concurrant, this fact is impossible for ABC non-degenerate. Y,...
