assume that all the lines that appear tangent are tangent. Find the perimeter.

We have that the tangents which meet at the same point outside the circle have the same length:
Then, in this case:
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