The figure shows a triangle ABC. L is a line through
the orthocenter H that cuts
the sides at A_{1}, B_{1}, and C_{1}. Lines A_{1}A_{2},
B_{1}B_{2}, and C_{1}C_{2} are the
reflection of L in sides BC, AC, and AB, respectively. Prove that A_{1}A_{2},
B_{1}B_{2}, and C_{1}C_{2} are
concurrent at a point P on the circumcircle O.
