设O1O2交AB于H AH=BH=c O1H=a O2H=b
a+b=12 (1)
a^2+c^2=(8√2)^2 (2)
b^2+c^2=4^2 (3)
(2)-(3) a^2-b^2=112
即 (a+b)(a-b)=112
将 (1)代入 12*(a-b)=112
a-b=28/3 结合(1)
得 a=32/3 b=4/3
代入(3)得 (4/3)^2+c^2=4^2
c=8√2/3
2c=16√2/3
即AB=16√2/3谢谢啦！~~~不客气