Prove that the two circles shown below are similar.

Question

anonymous · Answer

All circles are similar

anonymous · Answer

attachment

cwrw238 · Answer

all circles are similar (same shape)

anonymous · Answer

Yeah, I'm just not sure if they wanted me to do something else? They did add a diagram

anonymous · Answer

Nope. All you have to say is that all circles are similar to each other because they are all the same shape

anonymous · Answer

@jim_thompson5910

anonymous · Answer

@cwrw238 Do you think they want me to prove it otherwise?

jim_thompson5910 · Answer

hint: draw in triangles like so

anonymous · Answer

I'm lost ; ;

mokeira · Answer

the triangles will both exhibit Pythagoras' theory
probably will have a common ration which you can find

jim_thompson5910 · Answer

are you able to prove the two triangles are similar?

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

oh that's right, I remember now

jim_thompson5910 · Answer

so you weren't able to prove the triangles similar?

anonymous · Answer

Idk If finding the area of the circles would help or not. And no not yet, been stuck on this one for about a day now.

jim_thompson5910 · Answer

no you don't need to find the area

anonymous · Answer

Hmm. Then I'm really stuck

phi · Answer

one way to show two shapes are similar is to scale one of the shapes and then show they are congruent.

two circles are congruent if they have the same radius.

so this boils down to finding a scale factor to multiply the radius of one circle to get the radius of the other circle.

jim_thompson5910 · Answer

this video may help https://learnzillion.com/lessons/2688-establish-circle-similarity-using-similar-triangles it explains how to use triangles to prove all circles are similar

anonymous · Answer

Circle E radius is 3, c is 4

phi · Answer

so the scale factor is 4/3

anonymous · Answer

1.333

phi · Answer

you could say:  scale circle E by 4/3
translate horizontally -7 and vertically -8
the two circles will lay on top of each other... therefore congruent.
because we were able to apply a scale factor and translation, this shows they were similar

anonymous · Answer

Sweet, thank you both !

anonymous · Answer

The translation was in a lesson previously, starting ti make a little mroe sense

phi · Answer

More clearly,
If we are able to apply a scale factor and translation so that the two circles lay on top of each other, the two circles (by definition) are similar.