Be cause the ratio circumference:diameter is the same for every circle, is the ratio circumference:radius the same for every circle?

Absolutely! You have just unlocked one of the great

immutable secrets of the universe.

Ratio of

[ circumference / diameter ] =

ratio of

[ circumference / (2 x radius) ] =

(1/2) ratio of

[ circumference / diameter ].

I don't know how else to say it, so I hope that did it for you.