Tangent circles

Geometry Level 4

Two circles are tangent to each other, and their diameters \(d_1\) and \( d_2\) satisfy \(d_1 \times d_2=36\).
Segment \(AB\) is tangent to both circles. Find the length of \(AB\).

If you think that the length of \(AB\) depends on the relative values of \(d_1\) and \( d_2\), submit your answer as 9999.

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