Question

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.

Answer 1

@Jack1 please help

Answer 2

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

Answer 3

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

Answer 4

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 ;(

Answer 5

thanks anyway but do you know anyone who can?

Answer 6

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

Answer 7

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

Answer 8

thanks for trying to help man!:)

Answer 9

@ganeshie8 please help

Answer 10

@dan815 could you help me on this question please?

Answer 11

anyone please help!

Answer 12

@phi

Answer 13

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

Answer 14

@phi i really need help with this question!

Answer 15

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.

Answer 16

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

Answer 17

okay

Answer 18

circles are always similar tho, right...?

Answer 19

yes

Answer 20

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

Answer 21

okay then what?

Answer 22

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.

Answer 23

do I have to determine a rule?

Answer 24

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...

Answer 25

oh okay sorry.

Answer 26

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

Answer 27

or not at all?

Answer 28

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"

Answer 29

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

Answer 30

they ask, "Prove that the two circles are similar."

A proof would be doing all the things I just posted.

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

I'm still really confused

Answer 35

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

Answer 36

yes. Try to use your own words.

Answer 37

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"

Answer 38

?

Answer 39

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

Answer 40

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

Answer 41

oh okay thank you!:)

Answer 42

it says prove so that would be my proof?

Answer 43

yes

Answer 44

oh okay double checking! thanks again!:)

Answer 45

@phi
awesome work!