Question

Circle A has a radius of 2 inches, and circle B has a radius of 5 inches. Prove that the two circles are similar.

Answer 1

@SolomonZelman... I believe that if the circles are not congruent, then they are similar, with the similarity ratio given by the ratio of their radius. The ratio for these similar circles is 2:5. Also, it can be proved to be similar if their properties of perimeter, area and radius differ by some constant scale.

Answer 2

but I want to make sure this is right

Answer 3

@paki @robtobey

Answer 4

The ratio of the radii is the same as the ratio of the circumferences.
The ratio of the areas is the square of the ratio of the radii.

Answer 5

why do we need to prove when circles are always similar ....
though the radiis are always in the ratio .....

Answer 6

@jacquyjyz

Answer 7

What you believe is correct. If they are congruent, they are not similar, because they are not JUST similar (this is how I would put it).
And if they are congruent, then they are (only) similar.

Answer 8

I mean and if they are *not congruent

Answer 9

Congruent figures are always similar.
Similar figures are not always congruent.

Answer 10

yes, but when taking about the figure you wouldn't say that it is similar and grunet, if you can just say that it is congruent. Well.. idk about you, but I would not.

Answer 11

I agree with you. When you say two figures are congruent, you don't need to mention they are similar because it is understood they are also similar. When you state two figures are similar, you are trying to say they are only similar but not congruent.

Answer 12

Here, the radii have a certain ratio.
Show the circumferences have the same ratio, and show that the areas have the square of the ratio of the radii.