The ellipse conjecture for interior points associated with circumcenters

Let $ABC$ be a triangle, and let $D$ be a point such that $A,B,C,O_A,O_B,O_C$ lie on a conic, where $O_A$, $O_B$, and $O_C$ are the circumcenters of triangles $BCD$, $ACD$, and $ABD$, respectively.

Ellipse conjecture. The set of all interior points $D$ of the triangle $ABC$ satisfying this condition is an ellipse.

This problem arises in the study of geometric loci defined by conics and circumcenters. The source presents the assertion as a further-research problem, and no resolution is supplied here.