Dear Tuan

[BQT]

> I have got a very nice first result:

> - Q is fixed and is incenter I

> - Line is OH

> The locus (or at least all points on this line) is line connected

> mittenpunkt and Gergonne point.

That is,

Let ABC be a triangle, and P a point.

The perpendicular to IA through P intersects AB,AC at Ab,Ac, resp.

Similarly Bc,Ba, and Ca,Cb.

The locus of P such that the OH lines (Euler Lines) of PBcCb, PCaAc, PAbBa

are concurrent is Mittenpunkt-Gergone Line + ???

Probably the complete locus is some Cubic = Conic + Line

Nice result, indeed!

Antreas

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