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:

a. ratio of the diameter to the radius
       the ratio of the diameter to the radius for any circle is always going to be 2:1          because the diameter is 2 times the legnth of the radius any time so A is not                the right answer

b.  the degrees of the circle is always 360, the circumference is the distance around the circle, so that would be a good indicator since 360 is constant, but the circumference can change, and if they are the same, then the circles are similar. so B is the right answer

c.  Ratio of area to circumference. area=pir^2, and circumference=2pir
this is a good indicator becuase the ratio of the area and the circumference is different for every circle so c is the right answer

D.  the ratio of the diameter to the circumference  diameter=2r circumference=2pir
circumference=pi time diameter so the ratio of the diameter is 1:pi
this is not a good indicator so this is not the right answer

The answers are B and D, but if the teacher asks for only one, then I would pick c