The figure below shows
a quadrilateral ABCD with similar triangles ABC_{1}, A_{1}BC,
CDC_{2}, and A_{2}DA. M_{1}, M_{2}, M_{3}, and M_{4} are the midpoints of AC_{1},
A_{1}C, CC_{2}, and AA_{2}, respectively. M_{1}M_{3} and M_{2}M_{4} meet at O. Prove
that: (1) angle M_{2}OM_{3} = angle ABC_{1}; (2)
.
