This is a tantalizing problem from the 1977 Crux Mathematicorum.
“278. Proposed by W.A. McWorter, Jr., The Ohio State University.
If each of the medians of a triangle is extended beyond the sides of the triangle to 4/3 its length, show that the three new points formed and the vertices of the triangle all lie on an ellipse.”
See the Elliptical Medians Problem