Let ABC be an obtuse triangle, and let H denote its orthocenter. Let ωA denote the circle with center A and radius AH. Let ωB and ωC be defined in a similar way. For all points X in the plane of triangle ABC let circle Ω(X) be defined in the following way (if possible): take the polars of point X with respect to circles ωA, ωB and ωC, and let Ω(X) be the circumcircle of the triangle defined by these three lines.
With a possible exception of finitely many points find the locus of points X for which point X lies on circle Ω(X).Proposed by Vilmos Molnár-Szabó, Budapest geometrycircumcirclepoles and polars