Is the perimeter of equilateral triangle T equal to the circumference

This is a tricky one

Let's say t = a side of the equilateral triangle T
P = perimeter
C = circumference

Statement I

Sum of the lengths of a side of T and the radius of C is 9.
-> t + r = 9 => r = 9 - t
-> perimeter = 3t
-> circumference = 2(pi) (9-t)
-> 3t = 2(pi)(9-t)
-> 3t = 18pi - 2(pi)t
-> 3t + 2(pi)t = 18pi
Without doing the actual calculation, you should be able to infer that they can equal to each other, which means that perimeter and the circumference can equal to each other. Unfortunately this information is rather useless because it doesn't narrow down your answer. This statement essentially says that (could be) P < C or P = C or P > C

Statement II

The length of a side of T is equal to the diameter of C.

This statement sets up a distinct relationship
-> 3t & t*pi
Since pi is greater than 3, the circumference of the circle C cannot equal to perimeter of the triangle T. 3t cannot be greater than t*pi (because t > 0). Therefore Sufficient

Statement 2 on its own conclusively proves that they cannot equal to each other, but statement 1 doesn't. Therefore, the answer has to be (B)

This is how I see it, but I could be wrong. I think it's way more complicated than it needs to be which always makes me nervous about my answer. Let me know if I'm wrong somewhere.