Tangents
Initial explanation
We have that the tangents which meet at the same point outside the circle have the same length:
Tangents in this case
Then, in this case:
Perimeter
Now that we have all the measures, we find the perimeter just by adding them:
6 + 6 + 9 + 9 + 12+ 12 = 54
Answer: the perimeter of the figure is 54