Question

(will medal and fan)

Prove that the two circles shown below are similar.

Circle A is shown with a center at 3, 4 and a radius of 5. Circle C is shown with a center of 0, negative 1 and a radius of 2.

Answer 1

I'm thinking that I have to use right triangles. I know that because they're both circular, they're already similar to a certain extent. I need to go beyond that and use a different method to prove their similarity.

Answer 2

all circles are similar

Answer 3

but yeah if you want you can use right triangles, find that they are similar, and then say that the circles are similar

Answer 4

I think you have to translate one so they're both have the same center, then you dilate to make it the same size.

You could shift the small one right 3, up 5.

Answer 5

@agent0smith ok, I'll try that

Answer 6

@agent0smith I tried that, and while they are similar, I need to be able to explain my work in a way that wouldn't require a graph.

Answer 7

That doesn't make a whole lot of sense, considering you're given a graph.

Just show that they have the same ratio for their radii (find the radius of each), as for their circumference (find the circumference of each).

Answer 8

ALL circles are similar

they can be transformed by a translation and a scale

this is sufficient to prove similarity

Answer 9

@agent0smith
your method does not prove similarity - all circles meet that criterion - it is pi

Answer 10

lol but @MrNood that's what i gave her in the first place