Question

Intuitively, does it make sense that all circles are similar?

Answer 1

Answer:

Step-by-step explanation:

I think it does. A circle is the locus of all points that are equidistant from a fixed point (the center). The formula for a circle's circumference is C=2 pi r.

2 and pi are both constants. The only thing that changes is r and when it does C changes with it. There is no exception to similarity except if r = 0 in one case and r = anything else in another, but 0 always creates grief. So to get rid of the problem, make a condition that neither r or r1 can equal zero.

It is like saying two triangles can be declared similar if all 3 sides from one  form corresponding ratios with the second triangles sides. It is assumed that no side will equal zero.