## anonymous one year ago I need help with this question...

1. anonymous

Prove that the two circles shown below are similar.

2. anonymous

i keep seeing these and am totally confused aren't all circles similar?

3. anonymous

|dw:1440510136349:dw| notice that E was moved to C so now we have a dilation of $\huge \frac{ r_1 }{ r_2 }$ which gives the scale factor.

4. anonymous

yes, you need to use a formula to move one over another and dilate it, but idk the formula

5. anonymous

Sorry about using the same color, but essentially just using a transformation this actually proves all circles are similar to each other.

6. anonymous

so, what formula would i use to translate it?

7. anonymous

I mean we could say $\pi = \frac{ C }{ 2r }$ making all circles the same

8. anonymous

and would the scale factor be 3/4?

9. anonymous

4/3

10. anonymous

ohh, alright

11. anonymous

So the trick here is knowing that translations and dilations are the same hence all circles are the same

12. anonymous

i found a new formula for translations

13. anonymous

$(x - h){^2} + (y - k){^2} = r{^2}$

14. anonymous

That's the equation of a circle

15. anonymous

oh

16. anonymous

You may use it though

17. anonymous

ok so how would i put this into words? each step i mean

18. mathmate

Perhaps try this: given circle E : (x-4)^2+(y-9)^2=3^2 h=-7, k=-8, scale factor = 4/3 so (x-4+7)^2+(y-9+8)=(3*(4/3))^2 gives (x+3)^2+(y-1)^2=4^2 which is the circle C

19. anonymous

$(x,y) \implies (x-h,y-k)$ and end up doing a dilation

20. anonymous

ok thanks you guys, i have more questions i'll post in a couple of minutes, i'd appreciate it if you could help me with those as well :)