The figure shows a triangle ABC with the
altitudes AA_{1}, BB_{1}, and CC_{1}. If B_{1}D
is perpendicular to AB, and B_{1}E is perpendicular to BC, prove that
DE is equal to the semiperimeter of the triangle A_{1}B_{1}C_{1}.
Note: The triangle A_{1}B_{1}C_{1 }
is called the orthic triangle of the triangle ABC.
