Dear Hyacinthists, let ABC be a triangle, I the incenter, D, E, F the feet of the A, B, C-bisectors, Ma the perpendicular bisector of AD, Q, R the points of...
19318
Francisco Javier
garciacapitan
Oct 3, 2010 5:45 am
Dear Jean-Louis, your perpector is X100, ANTICOMPLEMENT OF FEUERBACH POINT....
19319
jeanlouisayme
Oct 3, 2010 12:21 pm
Dear Mathlinkers, an article IN ENGLISH concerning a circle tangent to the incircle has been put on my website http://perso.orange.fr/jl.ayme vol. 6 A circle...
19320
bbblow
Oct 3, 2010 3:25 pm
0. Preliminaries - When cevian triangles of P and Q are concyclic we say that P,Q are cyclocevian conjugates. - Define mapping c:(x:y:z)-> (y+z:z+x:x+y),...
19321
bbblow
Oct 3, 2010 4:47 pm
Or, we can simplify it and think: given perspector of an inconic can we give barycentrics for its foci? (Note that the foci are isogonal) Or, more generally,...
19322
Francisco Javier
garciacapitan
Oct 3, 2010 5:08 pm
Following is #5041 by Antreas, but modified. I consider CENTROIDS instead CIRCUMCENTERS, beacuse centroids lead us to a interesting locus. LOCUS Let ABC be a...
19323
Philippe
chephip
Oct 3, 2010 7:57 pm
... Dear bbblow, Of course yes. Construction (with compass and straightedge) is detailed for instance at mathafou.free.fr/themes_en/conique8.html Note : 1)...
19324
ForumGeom
ForumGeom@...
Oct 4, 2010 2:07 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2010volume10/FG201013index.html The editors Forum...
19325
Jean-Louis Ayme
jeanlouisayme
Oct 5, 2010 7:53 am
Dear Hyacinthists, an article IN ENGLISH concerning "An aesthetic proof" has been put on my website http://perso.orange.fr/jl.ayme vol. 10 Sincerely Jean-Louis...
19326
bbblow
Oct 7, 2010 6:18 am
Dear Philippe, Thank you very much for your construction. I have succeeded emulating your construction up to the construction of axes, but I do not know how to...
19327
yakub.aliyev
Oct 7, 2010 7:38 am
Dear friends, please inform me if you know any simple method for the following problem: Suppose you have some finite (possible very small) arc of a conic....
19328
bbblow
Oct 7, 2010 8:14 am
Triangle ABC is given. Construct a circle Ka tangent to angle BAC internally, and similarly define Kb, Kc. (Each circle have degree of freedom 1) Construct a...
19329
bbblow
Oct 7, 2010 8:36 am
You'd probably know that 5 points are enough determine a conic. Hence taking five points from the small arc of the conic, we can actually reconstruct the...
19330
yakub.aliyev
Oct 7, 2010 9:16 am
Dear friend, you are right by saying that 5 points determine a unique conic. But, as I sad in my previous message, we cannot reach, or, as you sad, reconstruct...
19331
Vladimir Dubrovsky
vladubr
Oct 7, 2010 11:20 am
Dear Yakub, I think, this will work: take two pairs of parallel chords and draw two lines, a and b, joining the midpoints of each pair. By comparing distances...
19332
Francois Rideau
francoisride...
Oct 7, 2010 1:20 pm
For example, with Cabri , you choose 5 points on your small arc. You ask Cabri to draw the conic through these 5 points. After that, if you click on the conic,...
19333
Francois Rideau
francoisride...
Oct 7, 2010 1:27 pm
Any small part of a conic contained in a small open set U of the plane have infinitely many points which is enough to choose 5 points on your small arc and to...
19334
LuÃs Lopes
qedtexte
Oct 7, 2010 1:57 pm
Dear Hyacinthists, Using Court's notation (N = Nagel point) and X' is such XX'=2r and (X,X')\perp a (side a). X = intouch incenter, X_a = contact point side a...
19335
lzhou@...
lizhoupolk
Oct 7, 2010 1:59 pm
You can find a photo of mine with this question at http://www.maa.org/FoundMath/10week37.html I'm thinking of overlay a grid and use coordinates as well. ...
19336
Nikolaos Dergiades
ndergiades
Oct 7, 2010 8:13 pm
Dear Yakub, and dear friends. An old Greek philosopher, Demonax, said to two of his friends quarreling about something: Dear friends, don't you think that one...
19337
Philippe
chephip
Oct 8, 2010 12:05 pm
Dear bbblow, All the constructions you need are described somewhere in my pages (browsing through the given links and with the "prev" "parent" and "next" menu...
19338
yakub.aliyev
Oct 11, 2010 12:24 pm
Dear friends, given two concentric circles with center O and let A be a point different from O in the interior of both of the circles. A ray through A...
19339
Francisco Javier
garciacapitan
Oct 11, 2010 4:57 pm
I get a curve with an equation of the eight degree. The equation includes your curve and another extra heart-shaped curve. I am not able to separate these...
19342
Luis
luisgeometria
Oct 13, 2010 6:42 am
Dear Hyacinthists, Let H,G,L be the orthocenter, centroid and the De Longhamps point X20 of the triangle ABC. HaHbHc, GaGbGc and LaLbLc are the pedal triangles...
19343
Francois Rideau
francoisride...
Oct 15, 2010 12:43 pm
I think it is Neuberg who, the first, has studied the pedal triangles of points on a same line. He proved the existence of the equicenter that is to say a...
19344
Ricardo Barroso
ricardobca
Oct 16, 2010 8:24 am
Friends of Hyacintos: A new edition of trianguloscabri (eleven year) in http://personal.us.es/rbarroso/trianguloscabri/ with four problems. Greetings from...
19345
Nikolaos Dergiades
ndergiades
Oct 16, 2010 10:08 pm
Dear Francois, thank you for this information. My proof is the following. If a point P moves on a line L with speed the vector v and A'B'C' is the pedal...
19346
ForumGeom
ForumGeom@...
Oct 18, 2010 2:43 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2010volume10/FG201014index.html The editors Forum...
19347
Antreas
xpolakis
Oct 19, 2010 7:17 am
Le ABC be a triangle, (c) a curve on the plane of ABC, and P a point on (c). General Problem: Which is the envelope of the radical axis of the NPC of ABC and...
19348
jpehrmfr
Oct 19, 2010 8:57 am
Dear Antreas ... The comnon points between the NPC and the pedal circle of P are the centers of the rectangular circumhyperbolae through P and through P*...
