How do we know that value of one radian is same for every circle? or in other words, How do we know that for every circle, arc length when equal to radius will subtend equal angle at the center which is what we call 1 radian(57.29°)
similarly, what's the proof that for every circle, 360th part of the circumference will have same measure of rotation(1°) in all of the circles?
Essentially, what I'm asking is in the following image.
