The diagram shows a triangle ABC with the
altitudes AA_{1}, BB_{1}, and CC_{1}. A_{1}A_{2},
is perpendicular to AB, A_{1}A_{3},
is perpendicular to AC and AA_{4} is perpendicular to A_{2}A_{3}.
Similarly
BB_{4} is perpendicular to B_{2}B_{3}, and CC_{4} is perpendicular to
C_{2}C_{3}. Prove that AA_{4}, BB_{4} ,
and CC_{4} are concurrent.
