The figure shows a triangle ABC with
the excircles E_{A}, E_{B}, and E_{C} tangent to the
extension of sides at the points
A_{1}, A_{2}, B_{1}, B_{2}, C_{1},
and C_{2}. Lines CA_{1} and BA_{2} meet at A_{3},
AB_{1} and CB_{2} meet at B_{3}, BC_{1}
and AC_{2} meet at C_{3}. Prove that lines AA_{3},
BB_{3}, and CC_{3} are concurrent.
