In the figure, O_{1}, O_{2}, O_{3}, O_{4} are
the centers of the squares erected over the sides of a
quadrilateral ABCD. If M_{1}, M_{2}, M_{3}, and M_{4}
are the midpoints of O_{1}O_{2}, O_{2}O_{3}, O_{3}O_{4}, and O_{4}O_{1}, respectively, prove
that M_{1}M_{2}M_{3}M_{4} is a square.
