Re: [EMHL] loci of concentric isogonals
- Thanks, Bernard and Francisco!
A couple of related problems:
1. What is the locus of the circumcenters?
2. Do ETC centers X(i) and X(j) exist such that X(i), X(j) and their
isogonal conjugates (whether in ETC or not) are concyclic?
--- In Hyacinthos@yahoogroups.com, Bernard Gibert <bg42@...> wrote:
> 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]