# Fagnano's problem

Solution to Fagnano's problem.

Fagnano's problem is as follows: in a given acute triangle *ABC*, find
the inscribed triangle whose perimeter is as small as possible. The answer is the **orthic triangle** of *ABC*, that is, the triangle (*DEF*) whose vertices are endpoints of the altitudes from each
of the vertices of *ABC*. The problem was proposed and solved using calculus by Giovanni Fagnano (1715–1797)
in 1775. Once the answer became known, several purely geometric solutions
were also discovered.