The figure below shows a triangle ABC and a
triangle A_{1}B_{1}C_{1} so that A_{1}A_{2}, B_{1}B_{2}, and C_{1}C_{2} are perpendicular
to BC, AC, and AB, respectively, and are concurrent at O_{1}. If
AA_{3}, BB_{3}, and CC_{3}, are perpendicular to B_{1}C_{1}, A_{1}C_{1}, and A_{1},B_{1},
respectively, prove that AA_{3}, BB_{3}, and CC_{3} are concurrent at O_{2}.
