What is the smallest perimeter of a triangle that can be inscribed in a triangle with sides of lengths $5$, $9$, and $10$?
I have read that such a triangle has its vertices at the feet of altitudes from the three vertices of the given triangle. (I guess the given triangle must be an acute triangle.) What is an efficient computation for the location of the vertices of the inscribed triangle.
I would appreciate a link to a demonstration that the triangle with its vertices at the feet of altitudes from the three vertices of a given triangle is a triangle with the smallest perimeter that can be inscribed in it.