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 orthocentric triangle, that is, the triangle whose vertices are the feet of the altitudes of the given triangle. The problem was posed by G. Fagnano dei Toschi in 1775.
- H. S. M. Coxeter, S. L. Greitzer, "Geometry Revisited", Mathematical Association of America (1967) ISBN 0883856190 Zbl 0166.16402
Fagnano problem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Fagnano_problem&oldid=42288