Interesting question generates interesting result:
The rectangular circumhyperbola passing through A, B, C, H and P* has center at concurrent point Q.
Here H is orthocenter of ABC, P* is isogonal conjugate of P wrt ABC and P* is also orthocenter of triangle PaPbPc.
Bui Quang Tuan
"Antreas P. Hatzipolakis" <xpolakis@...
> wrote: Dear Tuan
> Let ABC be a triangle, HaHbHc its Euler triangle, P = (x:y:z) with
>respect >ABC, a point, and Pa, Pb, Pc, the corresponding points with
>respect AHbHc, >BHcHa, CHaHb, resp.
> Now I try to connect Pa, Pb, Pc with the vertices of Euler
>triangle Ea, Eb, >Ec, the circumcenters of AHbHc, BHcHa, CHaHb.
> The result is very nice: with any P point = (x:y:z), three lines
>PaEa, PbEb, >PcEc are always concurrent at one point, say Q, on the
>nine point circle. The >locus is whole plane.
and I am wondering the point of concurrence
whose r. c/hyperbola the center is.
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