Which method is valid for proving that two circles are similar?

a- calculate the ratio of the diameter to the radius for each circle and show that they are equal.
b- calculate the ratio of degrees to the circumference for each circle and show that they are equal.
c- calculate the ratio of the área to the circumference for each circle and show that they are equal.
d- calculate the ratio of the diameter to the circumference for each and show that they are equal.

First I'm going to go through the choices with you and evaluate
each one.  Then after that, I'm going to hand you a secret that
I promise is going to knock your socks off.

a- Calculate the ratio of the diameter to the radius for each circle
and show that they are equal.
-- That won't tell you anything. The ratio of the diameter
to the radius of EVERY circle is 2 .

b- Calculate the ratio of degrees to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything.  The circumference
of EVERY circle subtends a central angle of 360°.

c- Calculate the ratio of the área to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything.  The ratio of the area
to the circumference of EVERY circle is (radius/2). 
They're only equal if the circles are the same size.

d- Calculate the ratio of the diameter to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything.  The ratio of the diameter
to the circumference of EVERY circle is  1/pi.   If the ratio isn't
1/pi, then you're not looking at a circle. 

None of these choices tells you whether the two circles are similar.
What are you going to do ?  How can you tell ? ?

Here's the surprise I promised you.
Beware of flying socks:

All circles are similar to all other circles.

Good night.