Circle B has a center of (−1, 5) and a radius of 4. Circle D has a center of (7, 4) and a radius of 2. Prove that the two circles are similar.

- anonymous

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- anonymous

@Jack1 please help

- Jack1

similar how...? all circles are similar...? circle d is just like 1/2 the size of circle b, sáll

- anonymous

I know i'm just confused on this question!:/

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- Jack1

i dont really understand... with triangles they can have different shapes so it makes sense when trying to prove they're similar... but all circles are the exact same shape... i dont get it either, sorry ;(

- anonymous

thanks anyway but do you know anyone who can?

- Jack1

@ganeshie8 lil help if u have a sec man, i'm lost on this one dude...?

- Jack1

or @dan815 ? u got a sec? how are circles "similar"?

- anonymous

thanks for trying to help man!:)

- anonymous

@ganeshie8 please help

- anonymous

@dan815 could you help me on this question please?

- anonymous

anyone please help!

- anonymous

@phi

- Jack1

@IrishBoy123 ur pretty cluey, du u understand this Q man?

- anonymous

@phi i really need help with this question!

- phi

similar means the objects have the same shape (but possible different sizes)
if we take two objects and "scale" one to be the same size as the other, and then show they can be laid on top of the other, that would show they are similar.

- IrishBoy123

https://www.illustrativemathematics.org/content-standards/tasks/1368
is any of this familiar to you
you move one circle onto the other and shrink or enlarge it to prove they are similar

- anonymous

okay

- Jack1

circles are always similar tho, right...?

- anonymous

yes

- phi

I would start with
Circle B has a center of (−1, 5) and a radius of 4
and translate (that means slide it) so its center is at (0,0)
(its shape will not change)
then shrink it by 2: its radius will go from 4 down to 2

- anonymous

okay then what?

- phi

next,
Circle D has a center of (7, 4) and a radius of 2.
slide D so its center is at (0,0)
its radius is 2, and it will lie directly on top of the other circle (which we moved to (0,0) and shrank to radius = 2)
this shows the two shapes are identical. Identical shapes mean the shapes are similar.

- anonymous

do I have to determine a rule?

- phi

a rule for what ?
there is the procedure to translate the circles and shrink (or expand) them so they lie on top of each other.
there is the "rule" that all circles are similar...

- anonymous

oh okay sorry.

- anonymous

do i just picture this in mind or do i draw it?

- anonymous

or not at all?

- phi

nobody else can read your mind, so you have to write down something.
I would sketch (graph) the original circles
then draw an arrow to show they are translated to the (0,0) origin
and write down "translate the center of the circle to (0,0)"
then show the two circles centered at the origin
then shrink the big circle by 2 (multiply its radius by 1/2)
and write "use dilation to change the size from radius 4 to radius 2"
then show a picture with both circles on top of each other, and write
"both circles lie on top of each other, and this shows they have the same shape"
"same shape means they are similar"

- anonymous

okay but that's not what it asks in my question! How about the other written part?

- phi

they ask, "Prove that the two circles are similar."
A proof would be doing all the things I just posted.

- Jack1

i;m still not understanding either @phi
couldn't we just right "they're circles : QED"?

- anonymous

but I can't take a picture of everything i just drew and put it in my question!

- phi

then just write the words that explain what you would do.

- anonymous

I'm still really confused

- anonymous

so i just put what you just wrote but in my own words?

- phi

yes. Try to use your own words.

- anonymous

so this part? would sketch (graph) the original circles
then draw an arrow to show they are translated to the (0,0) origin
and write down "translate the center of the circle to (0,0)"
then show the two circles centered at the origin
then shrink the big circle by 2 (multiply its radius by 1/2)
and write "use dilation to change the size from radius 4 to radius 2"
then show a picture with both circles on top of each other, and write
"both circles lie on top of each other, and this shows they have the same shape"
"same shape means they are similar"

- anonymous

?

- phi

@Jack1 I think this is some goofy "common core" idea. In Euclidean geometry I think it is assumed circles are similar

- phi

Yes Josh, but try to rewrite it using your own words.

- anonymous

oh okay thank you!:)

- anonymous

it says prove so that would be my proof?

- phi

yes

- anonymous

oh okay double checking! thanks again!:)

- IrishBoy123

@phi
awesome work!

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