[EMHL] Re: A Triangle Hexagon
- Dear Antreas
> > Parametrization:
> > Let ABC be a triangle, H, O its orthocenter, circumcenter, resp.
> > and Pa,Pb,Pc points on AH,BH,CH, resp. such that
> > APa/ AH = BPa / BH = CPa / CH = t
> > Fa, Fb, Fc = the orthogonal projections of Pa,Pb,Pc on OA,OB,OC
> > Oa, Ob, Oc = the orthogonal projections of O on HA,HB,HC resp.
> > Are the lines FaOa, FbOb, FcOc concurrent for every t?
> > If yes, the which is the locus of the point of concurrence, as
> > t varies?
> Yes they allways concur; after some computations, it appears thatat
> the locus of the common point is a rectangular hyperbola centered
> the center of the Taylor circle. The hyperbola goes through H, theAs the circumcenter of OaObOc is obviously the NPcenter of ABC, the
> NPCenter, the Kosnita point X(54), X(185), X(1147)...
rectangular hyperbola above should be the Jerabek hyperbola of