The figure below shows an arbelos ABC (AB, BC, and AC are semicircles of centers O_{1}, O_{2},
and O) and the squares ABB_{1}B_{2} and BCC_{1}C_{2}.
If M_{1} and M_{2} are the midpoints of B_{1}B_{2}
and C_{1}C_{2}, respectively, prove that AM_{2}
and CM_{1} intersect at I, the incenter of the arbelos.
