AB, AC, BC - Vectors.
r - Radius.
Arctangent(y, x) - Coprocessor function FPATAN, calculates an angle between vectors A(x, y) and X(1, 0)(using y and x coordinates of the A point).

My algorithm:

d = Abs(VectorMultiply(AC, BC)) / AB
if (d >= r) then Write(Length(AB))
else begin
    s1 = Sqrt(Length(AC) * Length(AC) - r * r)
    angle1 = Arctangent(Sqrt(Length(AC) * Length(AC) -
             d * d), d) - Arctangent(s1, r);
    s2 = Sqrt(Length(BC) * Length(BC) - r * r)
    angle2 = Arctangent(Sqrt(Length(BC) * Length(BC) -
             d * d), d) - Arctangent(s2, r);
    s = r * (angle1 + angle2)
    Write(s1 + s + s2)
end

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Am I wrong?

I think if you'll get following test, then you'll get 4th.

1 2 0
3 3 0
0 0 0
2

The answer is 2.24 (not 2.30)

Thank's Anatoly, that helped me. Don't know, how I've missed this :)