In the figure below, circles O_{1}, O_{2},
and O_{3} are tangent to each other and to a line L at A, B, and E,
respectively. The circle O_{4} passes through A and B and is
tangent to circle O_{3} at F. Tangent to the circle O_{4} at the
midpoint of major arc AB meets O_{1}A and O_{2}B extended at D and C,
respectively. Prove that ABCD is a square.
