Dear Randy, The point at infinity of line O1O2 is X(526). The coordinates of O1 are shown below (T stands for twice the area of the triangle multiplied by...
A construction of X(84) and a general locus: http://anthrakitis.blogspot.com/2011/12/reflections-of-cevians-in-cevians.html Being the center X84 on Darboux...
Locus of P is circumcircle + McCay cubic. ... Francisco Javier García Capitán http://garciacapitan.99on.com El 2 de diciembre de 2011 23:14, Antreas...
Dear friends, 1) If two triangles ABC and A'B'C' have the same circumcircle and are perspective at P (A'B'C' is the circumcevian triangle of P relative to ABC)...
Dear Nikolaos, In the first case, Q is midpoint of P and O. This can be easily derived from the fact that [circumcenter of PBC'] is image of [intersection of...
Dear Sung Hyun thank you. Francisco Garcia answered me privately that Q in first case is mid point of OP after finding the barycentrics of Q. Yes, you are...
Hello, Sung and Nikolaos, In case 1), there exist two points P for which the six circumcenters are on a circle. These two points lie on the Euler line, its...
I was able to replace your polynomial of degree 14 with one of degree 6. The coordinates of O1 are cyclically symmetric, and the first coordinate is ...
Let ABC be a triangle, IaIbIc the excentral triangle and A'B'C' the extagents triangle [see it HERE<http://mathworld.wolfram.com/ExtangentsTriangle.html> ] Let...
On Sun, Dec 4, 2011 at 12:37 AM, Antreas Hatzipolakis ... One of the centers is O. The other one?? APH -- http://anthrakitis.blogspot.com/ [Non-text portions...
Dear Antreas, this is the Euler-Morley quartic Q002. http://bernard.gibert.pagesperso-orange.fr/curves/q002.html Best regards Bernard ... [Non-text portions of...
Dear all, Take a conic from pencil generated by Steiner inellipse and Orthic Axis squared. Circumconics with perspectors on this conic have equal eccentricity...
Dear Sung Hyun, ... that with perspectors the intersections of the circumcircle and the orthic axis. it is real when ABC is obtusangle. Best regards Bernard ...
This is the point S = {a (a^3 - a^2 b - a b^2 + b^3 - a^2 c - 2 a b c + b^2 c - a c^2 + b c^2 + c^3), b (a^3 - a^2 b - a b^2 + b^3 + a^2 c - 2 a b c - b^2 c +...
Dear Sung Hyun and Bernard ... Yes, very good. If you consider the feet U & V of the tangents from a point P to an inconic, the pencil of conics touching PU &...
Dear Jean-Pierre and Bernard, Big thanks to both of you for the interesting results. I'd like to throw another question: what is the value of (1-2e^{-2})^2 for...
Dear Sung Hyun Lim a remark : as the tangential triangle KaKbKc is the precevian triangle of K, the tangential triangle is selfpolar wrt your conic. Its...
Barycentrics of [point with coordinates (u:v:w) from perspective of tangential triangle] are K [Non-text portions of this message have been removed]...
Barycentrics of [point with coordinates (u:v:w) from perspective of tangential triangle] are K * anticomplement of [X div [anticomplement of K] ] where * is...
Dear Bernard Thank you. The email correspondace between Francisco and me took place after midnight, and it seems we were semi-sleeping :-) Antreas ... ...
Dear All My Friends, Point E is orthogonal projection of focus F on directrix of a parabola. The circle with diameter EF intersects the parabola at two...
Dear Sung Hyun and Jean-Pierre, ... Actually, the bicevian conic is bitangent to the Steiner inellipse at its intersections with the orthic axis but these...
Dear Bernard, Just a remark: Jean-Pierre also commented that this is a bitangent pencil in #19531. Regards, Sung Hyun [Non-text portions of this message have...
A construction of X(54) http://anthrakitis.blogspot.com/2011/12/reflections-of-circumcircle-in.html APH [Non-text portions of this message have been removed]...
Let ABC be a triangle, P a point, A'B'C' the pedal triangle of P, A12, A13 the orthogonal projections of the excenters I2, I3 on PA', resp.. Let A* = BA13 /\...
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forumgeom forumgeom
ForumGeom@...
Dec 5, 2011 6:24 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2011volume11/FG201128index.html The editors Forum...
