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22065Fwd: [EGML] Re: Point ?

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  • Antreas Hatzipolakis
    Mar 23, 2014

      ---------- Forwarded message ----------
      From: César Lozada 
      Date: Sun, Mar 23, 2014 at 7:03 AM
      Subject: RE: [EGML] Re: Point ?
      To: Anopolis@yahoogroups.com



       Z = ((36*R^2-7*SW)*SA^2+(-144*R^4-2*SW^2+38*SW*R^2)*SA+S^2*(-5*SW+24*R^2))*a :: (trilinears)

          = (5,113) /\ (110,1593)

          =  ( -4.440739185485755, -6.09447912568251, 9.909491192988773 )



      César Lozada





      De: Anopolis@yahoogroups.com [mailto:Anopolis@yahoogroups.com] En nombre de Antreas Hatzipolakis
      Enviado el: Sábado, 22 de Marzo de 2014 11:20 p.m.
      Para: anopolis@yahoogroups.com; Hyacinthos
      Asunto: [EGML] Re: Point ? [1 Attachment]





      On Sat, Mar 22, 2014 at 8:01 PM, Antreas Hatzipolakis <anopolis72@...> wrote:

      Let ABC be a triangle and AaBbCc its orthic triangle.



      Ab, Ac = the orthogonal projections of Aa on BBb, CCc, resp.



      A2 = the orhogonal projection of Ab on AaAc

      A3 = the ortogonal projection of Ac on AaAb


      L1 = the Euler line of AaA2A3.

      Similarly L2,L3 = the Euler lines of BbB3B1, CcC1C2, resp.

      ABC and the three triangles are homothetic, so their Euler lines are


      Now, the reflections of L1,L2,L3 in (altitudes of ABC) AAa, BBb, CCc,

      resp. are concurrent.