Fagnano's Theorem - Alternative Proof

Fagnano’s Problem: In 1775, Giovanni Fagnano posed and solved the problem - “For a given acute angled triangle, determine the inscribed triangle of minimum perimeter.” Using calculus, Fagnano showed the solution to be the Orthic Triangle – a triangle formed by the feet of the three altitudes. A different proof was given in At Right Angles, Vol. 6, No. 1, March 2017, available at http://azimpremjiuniversity.edu.in/ SitePages/resources-ara-march-2017-fagnanos-problem.aspx

Let’s see if it can be solved using geometry and a result from Physics called Fermat’s principle.

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