‘each point would be a side’ ... and you have a BS in Math? LOL it takes TWO points to determine a line thus it takes two points to determine the location of a side.
You’re right, I should have been more precise. Each point would cause a tangent line defining a side. Every tangent line/side would be unique to that circle.
Richard Feynman used that ‘principle’ to determine an orbit using only Algebra and trigonometry, ... if I’m remembering it right. An old man gets a pass on memory things, right?