Online Geometry Problem 735: Triangle, Altitude, Perpendicular,  Semiperimeter of the Orthic Triangle, Congruence. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a triangle ABC with the altitudes AA₁, BB₁, and CC₁. If B₁D is perpendicular to AB, and B₁E is perpendicular to BC, prove that DE is equal to the semiperimeter of the triangle A₁B₁C₁.
Note: The triangle A₁B₁C₁ is called the orthic triangle of the triangle ABC.