> The question: > Given an acute triangle, find the inscribed triangle (with one point > on each side of the original triangle) of minimum perimeter. > > The answer: > The triangle formed by the feet of the altitudes of the original > triangle has the smallest perimeter. > > The proof: > I don't know yet. > > --Joshua Zucker
But I do! This is a well-known theorem, and there's an easy proof by reflecting the triangle in its sides so as to convert the problem into a shortest path one (think of light bouncing around inside a triangle of mirrors).