Hey y'all, i need the exact explanation for why the two are similar despite them being two different sizes. you so

I've found similarity on circles is kinda phony and bogus and a little circular.

in short, a circle is just that, and any other circle by definition will be similar to it.

but the similarity statements go with translations and dilations, you move this guy this way and then that way, and voila, they're similar.

circle A's radius is dilated by some factor to turn into "s", and due to that the circle itself gets blown up.

it then gets translated over the x-axis some value, and over the y-axis some other value, and landed where circle B is at.

because of all that rigamarole, circle A ~ circle B.