Πέμπτη 12 Σεπτεμβρίου 2013

CONCYCLIC

RE: [EGML] CONIC - LOCUS

Posted By: cesar_e_lozada

Fri Sep 6, 2013 10:28 pm

Dear Antreas:

They are concyclic for all points P.

The center of their circle is the complement of the isotomic of P.

Regards

Cιsar Lozada

De: Anopolis@yahoogroups.com [mailto:Anopolis@yahoogroups.com] En nombre de Antreas Hatzipolakis

Enviado el: Jueves, 05 de Septiembre de 2013 06:28 p.m.

Para: anopolis@yahoogroups.com

Asunto: [EGML] CONIC - LOCUS

Let ABC be a triangle and A'B'C' the cevian triangle of P.

Denote:

Ab, Ac = the intersections of the circles with diameters BC, AA'

(near to B,C, resp.)

Bc, Ba = the intersections of the circles with diameters CA, BB'

Ca, Cb = the intersections of the circles with diameters AB, CC'

For P = H, the six points are concyclic.

For which P's are the six points lying on a conic?

APH

Anopolis #956


-

Δεν υπάρχουν σχόλια:

Δημοσίευση σχολίου

Εγγραφή σε: Σχόλια ανάρτησης (Atom)

ETC

X(72413) = X(1296)X(66615)∩X(8705)X(10098) Barycentrics    a^2*(2*a^10+2*b^10-b^8*c^2-11*b^6*c^4+5*b^4*c^6+9*b^2*c^8-4*c^10-a^8*(8*b^2...

  • EUCLID 4404
  • ETC
    X(5459) Let ABC be a triangle, let A', B', C' be the midpoints of BC, CA, AB. Let L_a be the perpendicular through A' ...
  • HOMOTHETIC TRIANGLES and EULER LINES
    Theorem 1. Let ABC be an equilateral triangle and P a point. The Euler lines of the triangles PBC,PCA,PAB are concurent.Denote the point ...