The problem in which one is required to inscribe a triangle of least-possible perimeter in a given acute-angled triangle. The solution is the so-called orthocentric triangle, that is, the triangle whose vertices are the feets of the altitudes of the given triangle. The problem was posed by G. Fagnano dei Toschi in 1775.
Fagnano problem. P.S. Modenov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Fagnano_problem&oldid=14231