Prove that the two circles shown below are similar

- anonymous

Prove that the two circles shown below are similar

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- anonymous

http://learn.flvs.net/webdav/assessment_images/educator_geometry/v15/module09/09_08_9.jpg

- anonymous

@is3535

- imqwerty

cookie error comes when i open the link

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## More answers

- anonymous

SAME WITH ME.

- anonymous

humm okay one sec let me screen shot the image and post it :p

- is3535

me to

- anonymous

##### 1 Attachment

- anonymous

there u go let me know if that works

- imqwerty

yes it works

- is3535

no ther no simliar B is 5 and D 7 i say

- anonymous

okay can yall help me? this is what i have so far.. idk if its right All circles are similar because you can scale one circle to be the same size as another (bigger or smaller) circle. They effectively have the same shape.

- is3535

im not 1000 % that i said

- anonymous

humm... i dont think that is right haha

- anonymous

you can go from one figure to the other with a translation and a dilation, does that make them similar?
im not so sure...

- anonymous

what if i say this??
Theorem: Any two circles are similar.
Proof: Given a circle of radius r and a
second circle of radius R , perform a
translation so that their centers coincide.
A dilation from the common center of the
circles with scale factor R takes the
points of one circle and maps them onto the
second.
Thus we have mapped one circle onto the
other via a translation and a dilation. The
circles are simila

- anonymous

First circle with center (-1,5) and radius=4
second circle with center (7,4) and radius =2

- anonymous

@CayleeS23 ... where did you get that theorem from?

- anonymous

Their similar because

- anonymous

http://www.jamestanton.com/wp-content/uploads/2012/03/Curriculum-Newsletter_January-2013.pdf

- anonymous

hello???

- anonymous

looks like they are similar, and the proof would be what @CayleeS23 posted before...

- anonymous

im confused...

- anonymous

listen

- anonymous

very simple

- anonymous

their both round and they both have no sides

- anonymous

proved

- anonymous

feel free to fan and medal me

- anonymous

no that doesnt prove anything haha get otta here dude...

- anonymous

i guess a better proof would be taking the ratio of their perimeter to their radius for each of them, you will get the same in both cases, actually you get:
\[2\pi\] for any circle
so they are similar

- anonymous

I tried. I failed/

- anonymous

hey
sometimes the answer is easier than you think

- anonymous

ohh okay that makes since so should i just put that?? proof would be taking the ratio of their perimeter to their radius for each of them, you will get the same in both cases, actually you get:
2π
for any circle
so they are similar

- anonymous

can u show me how u did that math? to prove that they are both 2pi

- anonymous

this is pi|dw:1433531216624:dw|

- anonymous

if you look for the definition of similarity you find somethng like this:
"Two figures that have the same shape are said to be similar.When two figures are similar, the ratios of the lengths of their corresponding sides are equal."
Applied to a rectangle you would use the ratio between the sides, because that is what defines the rectangle shape, for a circle, the important quantity is its radius

- anonymous

@Gunboss that is exactly what i was saying...

- anonymous

:D

- anonymous

hum okay... @Gunboss pi means 3.14 in math terms you are thinking of pie like food haha

- anonymous

I guess. (btw my pi is better)

- MrNood

Given a circle of radius r and a
second circle of radius R , perform a
translation so that their centers coincide.
A dilation from the common center of the
circles with scale factor
k=R/r
takes the
points of one circle and maps them onto the
second.
Thus we have mapped one circle onto the
other via a translation and a dilation. The
circles are similar.

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