Why would we use the radius of a circle instead of the diameter when calculating circumference? Forgive me if this question is a little too strange or maybe even off.  Mathematics has never been my strong point, but I definitely think it's the coolest...
Anyway, I was looking into tau, pi's up-and-coming sibling. I started rethinking why pi worked. The thing about tau is that it supposedly skips the step of doubling πr, since tau is twice pi. I tried this, and it works! (Of course it works. The fact that this surprises and amazes me shows how little I get out...)
Then I started wondering why we do 2πr instead of πd. It does give the same answer... I checked. Is there any reason why using the radius is preferred over using the diameter?
Here's my work:

r = 6 (ergo diameter must equal 12)
C = 2πr
C = 37.68
and...
C = Tr
C = 37.68
and...
C = πd
C = 37.68


There is actually a good reason for writing the circumference as $\pi d$ rather than $2\pi r$: the first formula actually holds for the perimeter of any closed curve of constant diameter $d$, not just for circles. An example of such a curve is the Reuleaux triangle.
