As is well-known, a Cevian triangle is the triangle formed by the intersections of a triangle's sides with their corresponding Cevians (a line through a point inside the triangle, i.e. the Cevian point, and the vertex opposite the side).
An application I'm considering requires me to reckon the Cevian triangle of smallest area with respect to the centroid of the triangle that is similar to the original triangle. For the equilateral case, the medial triangle is an "obvious" solution, but is the medial triangle the Cevian triangle with respect to the centroid that is similar and has the smallest area, or are there more "optimal" triangles?
I've tried searching around, but I am probably not using the right keywords. Any help would be lovely.