Cevians as sides of triangles (Q2714293)

The author considers the following problem in the Euclidean plane: Given a triangle \(ABC\) find the set \(S\) of all points \(X\) in the plane such that the three cevians of \(X\) are congruent to the sides of a triangle. (The cevians of \(X\) are the intersection of the convex hull of the triangle \(ABC\) with the lines \(AX\), \(BX\), and \(CX\), respectively.) It is shown that the boundary of \(S\) is an algebraic curve of order \(12\). Further, it is shown that the convex hull of certain triangle centres (according to a list due to \textit{C. Kimberling} [Math. Mag. 67, 163-187 (1994; Zbl 0821.51014)]) is a subset of the set \(S\).