, 2024

Let $ABC$ be an obtuse triangle, and let $H$ denote its orthocenter. Let $\omega_A$ denote the circle with center $A$ and radius $AH$. Let $\omega_B$ and $\omega_C$ be defined in a similar way. For all points $X$ in the plane of triangle $ABC$ let circle $\Omega(X)$ be defined in the following way (if possible): take the polars of point $X$ with respect to circles $\omega_A$, $\omega_B$ and $\omega_C$, and let $\Omega(X)$ 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 $\Omega(X)$.