因为圆心O是三角形ABC的内切圆,切点为D,E,F
则有AD=AE=1
BD=BF=2
CE=CF=3
AB=AD+BD=1+2=3
AC=AE+CE=1+3=4
BC=BF+CF=2+3=5
S△ABC=S△ABO+S△ACO+S△BCO
=1/2*AB*R+1/2AC*R+1/2BC*R
=1/2(3R+4R+5R)
=12R/2=6R=6
R=1