Equicevian points in a triangle (Q6631509)

A cevian in a triangle is a line that passes through one of its vertices. The length of a cevian is measured from the vertex to the point where it intersects the opposite side. If the lengths of three concurrent cevians are all equal, they are called equicevians, and their intersection point is called an equicevian point.\N\NAccording to a theorem by Abu-Saymeh, Hajja, and Stachel, triangles can have up to two equicevian points that do not lie on the sides of the triangle. These points are precisely the foci of the Steiner circumellipse of the triangle. The center of this circumellipse is the centroid of the triangle. The authors of this paper show that up to six additional equicevian points can lie on the sides of the triangle (or their extensions). All cases are classified, and the general result for isosceles triangles is proved geometrically.