Loading ...
Sorry, an error occurred while loading the content.

4891Re: [EMHL] The pedal triangles of Ia, Ib, Ic

Expand Messages
  • Boutte Gilles
    Mar 3, 2002
      Dear Antreas

      > Dear Gilles,
      >
      > [APH]
      > Let IaaIabIac be the pedal triangle of Ia.
      >
      > A' := IaIaa /\ IabIac
      >
      > Similarly B', C'
      >
      > The triangles ABC, A'B'C' are perspective.
      >
      > [...]
      >
      >
      > ==> the point of concurrence is the centroid G.
      >
      > [...]
      >
      > 1. A" := the orth. projection of Iaa on IabIac.
      >
      > Similarly B", C"
      >
      > Then the triangles ABC, A"B"C" are perspective.
      >
      > [GB]:
      > The triangle MaMbMc with sides IabIac, IbaIbc, IcaIcb is homothetic to
      > IaIbIc. A' is the feet on IabIac of the altitude, as we prove with
      > Nikolaos Dergiades.
      > A'B'C' is the orthic triangle of MaMbMc, and ABC is the orthic triangle
      > of IaIbIc. So ABC and A'B'C' are homothetic, therefore they are
      > perspective. Perspector is the Mittelpunkt X_9 of ABC.
      >
      > *********
      >
      > I guess your A'B'C' is mine A"B"C".


      I apologize, you are right.. I am mistaked in my notations.

      Gilles

      >
      >
      > Let's see what the perspector of ABC, A"B"C" is:
      >
      >
      > A
      > ..................
      > / \
      > / \
      > B----A1-Iaa--------C
      > / \
      > A3 A2
      > Iac \
      > / A" Iab
      > / \
      > Ia
      >
      > [...]
      >
      > ==> AA" is the a-cevian of Mittenpunkt (cot(A/2) ::)
      >
      >
      > Antreas
    • Show all 35 messages in this topic