To solve This Problem you should have patient
First You should change 3D into 2D. to do in 2D is easier of cause.
Second you should check whether it go through the ball
       if not, calc it directly;
       if so, to calc it which go through the tangent. it's shorter Of cause
At last , To check some Special case it will get AC.......
           Come on, my friends

> change 3D into 2D
>
This is what I did!
Then I check everything right as you say:

____if { thread is outside } then
________Result := { AB distance }
____else
________Result :=
____________{ tangent from A } + { tangent from B } +
____________{ a small arc between tangents }

And that's all!
I didn't check any 'special cases'...
I didn't care about them.
I didn't see them at all!
But I got AC (0.015 sec, 415 Kb), see here: http://acm.timus.ru/status.aspx?space=1&pos=851589.
So... I'd like to find it out, what are the special cases, that I missed...
Can you tell me, please?