The figure shows equal circles A, B,
and C. AA_{1}, AA_{2}, CC_{3}, and CC_{4}
are tangents to circle B, AA_{3}, AA_{4}, BB_{3},
and BB_{4} are tangents to circle C, and BB_{1},
BB_{2}, CC_{1}, 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_{1}, BB_{3}
with CC_{3}, AA_{4} with CC_{1}, AA_{2}
with BB_{2}, BB_{4} with CC_{4}, and AA_{3}
with CC_{2}, respectively. Prove that (1) The extension
of DG, EH, and FM are concurrent, (2) If s is the semiperimeter
of the hexagon ADBECF, then s = AD + BE + CF = BD + CE + AF.