# Fagnano problem

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Fagnano problem. P.S. Modenov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Fagnano_problem&oldid=14231

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098