I placed six points on the circumference of a circle such that the distance between any two of the points is an integer. What is the smallest such circle I could use?

What if each distance must be unique?

I'd agree that the shortest distance is a line, but I believe that the
authors intent was to measure the distance along the circumference -
though then it doedsn't really seem like a level 4 puzzle...

Also, no one has picked up that 0 is an integer - therefore, part one
is a circle of diameter 1/infinity, with all points coincident (this
also makes the method of measurement irrellevant). Doesn't work
for part 2.