Yes, it's true that cutting building materials in circles would be very hard, but there are some circular things you could use as a "base" to build on. Even then, I'm not sure how that would work. I haven't actually built a coop technically, so this is just theoretical.
I recently saw a math problem that was something like this:
The farmer has enough material to make a corral for his animals with a perimeter of 21 feet. What shape should he make his corral so he will get the most area?
The shapes with the most area were a square and circle, but how would you...