The figure shows equal circles A, B,
and C. AA_{1} and CC_{1}
are tangents to circle B, AA_{2} and BB_{1} are
tangents to circle C, and BB_{2} and CC_{2} are
tangents to circle A. Points D, E, F, G, H, and M are the
intersection points of the tangents AA_{1} with BB_{2},
AA_{1}
with CC_{1}, BB_{1} with CC_{1}, BB_{1}
with AA_{2}, CC_{2} with AA_{2}, and CC_{2}
with BB_{2}, respectively. If s is the semiperimeter of
the hexagon DEFGHM, prove that s = DM+EF+GH = DE+FG+HM.