Fagnano's Problem

In a given Acute-angled Triangle $\Delta ABC$, Inscribe another Triangle whose Perimeter is as small as possible. The answer is the Orthic Triangle of $\Delta ABC$.

References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 88-89, 1967.