Circle A has center of (0, 4) and a radius of 6, and circle B has a center of (-3, 5) and a radius of 24. What steps will help show that circle A is similar to circle B?

Question

anonymous · Answer

@Preetha @sleepyjess

anonymous · Answer

I need someone else's opinion I'm stuck

anonymous · Answer

Aren't all circles simialr?

sleepyjess · Answer

I never thought I would be in the same tag as preetha lol

anonymous · Answer

similar

sleepyjess · Answer

And I agree with @eliassaab

sleepyjess · Answer

@amistre64 Can you confirm this?

amistre64 · Answer

the steps to show that one circle is similar to another is not simply stating that they are similar ...

anonymous · Answer

Yes, but I have to pick one of the multiple choice

amistre64 · Answer

how do we show things are similar?  what is your definition?

amistre64 · Answer

one definition may be:  2 things are similar if one can be transformed into the other only by dilation

anonymous · Answer

Translate circle A using the rule (x+3, y−1). Rotate circle A 180° about the center. Dilate circle A by a scale factor of 4. Reflect circle A over the line y=x.

amistre64 · Answer

well, that might be a technically bad definition on my part, since moving objects from one place to another is valid since the structure isnt changed.

amistre64 · Answer

if we have 2 circles, and move them so that they center about the same point; then we can dilate one circle into the other in a general way to prove that all circles are similar to each other

amistre64 · Answer

no need to rotate a circle ...  but other than that, it seems fair to me

amistre64 · Answer

if we can determine a center of dilation, then moving the circles becomes redundant as well

amistre64 · Answer

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anonymous · Answer

No those are four different choices lol
1. Translate circle A using the rule (x+3, y−1). 
3. Dilate circle A by a scale factor of 4. 
4. Reflect circle A over the line y=x.

anonymous · Answer

So you think it's dilate by four as well?
It's not translate circle A?

amistre64 · Answer

if we are given to only one process, dilation is the most important yes.

reflecting does nothing for us,  and translating doesnt prove similarity, but does help in getting them to a more accessible dilation point is all.

its dilation that is the important process to me

anonymous · Answer

Thank you so much!

amistre64 · Answer

if we ignore centers, then dilating a radius if 6 into a radius of 24 to get congruent cirlces is acceptable yes

C1 = 2pi (r1) 

C2 = 2pi (r2)

in order for a dilation of C1 to equal C2

d C1 = C2

d 2pi r1 = 2pi r2

d  r1 =  r2

d = r2/r1

therefore d = 24/6 in this case