Dear Antreas,

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.

Best regards,

Bui Quang Tuan

"Antreas P. Hatzipolakis" <

xpolakis@...> wrote: Dear Tuan

[BQT]

> 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.

APH

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