Question

Prove that the two circles shown below are similar.

Answer 1

I know all circles are similar, but how can i show the proportions are similar?

Answer 2

@ganeshie8

Answer 3

Find the radius of each circle. It shows the center, so you can find the radius since it's on a graph

Answer 4

4 and 3?

Answer 5

If you REALLY want, you can show that the Radii have the same ratio as the circumferi.

No, that's not a word.

...or that the Areas have the ratio squared.

Radius Ratio: 3:4
Circumference Ratio: 3:4
Area Ratio: 9:16

Answer 6

yeah it's 4 and 3. tkhunny showed how to prove it from there.

Answer 7

There really is no "proving", per se. All circles are similar, after all. These are just the little pieces that are easily demonstrated.

Answer 8

What about through dilating ?

Answer 9

I'm just having trouble putting together a response from the info i got..

Answer 10

Well, like with a triangle, you can have all the angles equal each other so you have similar triangles. You can prove it with ratios of the angles. With a circle, they are all similar, so you should be able to show the radii of each circle. There are a ton of ways to show they are similar. I would put radius of E=3, radius of C=4. then find the area of the circles and compare those.

Answer 11

Area of E is 28.27
Area of C is 50.27

Answer 12

You can write a three-function transformation if you like.

Starting with the larger...
1) Dilation Factor of 3/4 centered at (-3,1)
2) Horizontal shift +7
3) Vertical shift +8

I guess that would look better on your assignment that, "Well, of course they are similar! Why would you ask such a stupid question, you idiot?!" That might be too colloquial and flippant for serious academic work. :-)

Answer 13

Confused now x.x But yeah idt she would like that response haha @tk

Answer 14

50.27/28.27 = 1.78
16/9 = 1.78
Perfect. I would have preferred more decimal places, but that's fine.

Answer 15

according to Eclids geometry
all circles are similar. you already know that >.<

Answer 16

how did you get 16/9 @tkhunny

Answer 17

Repeated from WAY above:

Radius Ratio: 3:4
Circumference Ratio: 3:4
Area Ratio: 9:16