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.

Question

Breiland287 Breiland287

15-05-2015
Mathematics

Answered

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.

Answer :

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apologiabiology apologiabiology · Answer 1 · 2015-05-15T14:52:25-04:00

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