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

21876Re: [EMHL] loci of concentric isogonals

Expand Messages
  • Bernard Gibert
    Apr 1, 2013
      Dear Randy,

      > Given two fixed isogonal points, X and X', and two variable isogonal
      > points, P and P', what is the locus of P such that X, X', P, P' are
      > concyclic?
      > Special cases: X,X' = G,K; O,H; 1st and 2nd Brocard points?

      I find a bicircular isogonal circum-sextic passing through the in/excenters, X, X', the intersections of (O) and the line XX', their isogonal conjugates at infinity.
      A, B, C, X, X' are nodes.

      When X lies on (O), the sextic splits into (O), the line at infinity and the pK(X6, X). See


      These sextics seem to be not very prolific in ETC centers, in particular your special cases.

      There are 3 bicircular isogonal circum-sextics in CTC but none of them corresponds to this configuration.

      Who's going to find a nice one ?

      Best regards


      [Non-text portions of this message have been removed]
    • Show all 3 messages in this topic