Problem

Source: Cono sur Olympiad 1997 P6

Tags: geometry, geometry unsolved



Let $ABC$ be a acute-angle triangle and $X$ be point in the plane of this triangle. Let $M,N,P$ be the orthogonal projections of $X$ in the lines that contains the altitudes of this triangle Determine the positions of the point $X$ such that the triangle $MNP$ is congruent to $ABC$