Question

Circle C has a center of (−3, 1) and a radius of 4. Circle E has a center of (4, 9) and a radius of 3. Prove that the two circles are similar.

Anyone please help me with this? @amistre64 @Hero @ash2326 @Luigi0210

Answer 1

@Whitemonsterbunny17

Answer 2

what is your definition of similarity?

Answer 3

i can see it as side-angle-side ...

Answer 4

but thats congruent .... similar is any scalar variety

Answer 5

move each circle to the center, and scale one to get the other .... but like a stated first, depends on your definition of similar

Answer 6

well i went to see how to do this on geogebra as it says in my lesson to create a circle with a center of the given coordinates and whichever radius so i did that with both the circles and tried to translate it to lie on the same center point of circle B but i didn't know ho to. @amistre64

Answer 7

thats why i just move them to the center ... if we are allowed to move one object, we are allowed to move both objects ...

Answer 8

x^2 + y^2 = 4^2

and

x^2 + y^2 = 3^2

the one is just a scalar of the other by 4^2/3^2

Answer 9

so thats how i prove that the circles are similar?

Answer 10

thats how I would do it, but im not the one doing a specifically instructed assignment

Answer 11

the assignment just gave us the center coordinate points and their radiuses and said to prove that the 2 circles are similar. @amistre64

Answer 12

@amistre64

Answer 13

@Hero

Answer 14

@amistre64

Answer 15

@amistre64

Answer 16

@agent0smith

Answer 17

All circles are similar...

Answer 18

yeah prove it is what the question is asking.. i know that all circles are similar.

Answer 19

translating something is just moving it about the grid ...

so if we 'move' both centers the the origin (0,0) we have moved one on top of the other ....

Answer 20

can u show me how on geogebra cuz i tried its not working...

Answer 21

i dont know how to work geogebra ...

Answer 22

but the concept i have in mind is this:



take some random point on one of the circles, we form a triangle with it .... which can then be scaled to find a spot for it on the other circle.

Answer 23

since x = rcos(t) and y = r sin(t) some (a,b) on the 3rad circle is just:

a = 3cos(t), b = 3sin(t)

multiply by 4/3 to scale it to the 4rad circle

4a/3 = 4cos(t), 4b/3 = 4sin(t)

now a' = 4a/3 and b' = 4b/3 for the point that is similar on the other circle.

Answer 24

but im not sure how geogebra works to use this idea

Answer 25

this is what it says on my lesson

Answer 26

and thats what i demonstrated, except i moved both to center at 0,0 indtead

Answer 27

*instead

Answer 28

the scale factor ak = a' is when k=4/3 tom scale from 3 to 4

Answer 29

x^2 + y^2 = 3^2 , for some point (a,b)

4^2/3^2 * (a^2 + b^2 = 3^2)

(4a/3)^2 + (4b/3)^2 = 4^2

therefore, by using a dilation factor of k: ak = a'

4a/3 = a', k=4/3

Answer 30

but how does that prove theyre similar?

Answer 31

thats why i said it depends on your definition of similar ... your file suggests that the definition is that a dilated objects are similar to each other.

Answer 32

our dilation factor to get from a to a' is 4/3 and to get from b to b' is 4/3; so we have demonstarted that we can get from one point (a,b) on one circle to a point (a',b') on the other circle by a dilation of 4/3

Answer 33

ok but for the assignment i have to dilate circle A to lie on the center point of circle B so when i dilate it on geogebra and it asks for the factor should i just type 4/3 in?

Answer 34

maybe, but i dont know how to use geogebra so asking me how to do somehting with geogebra is futile.

Answer 35

a center of dilation is key ..... which is why i simply made both centers at the origin

Answer 36

yeah thats my problem now.. my lesson has the example using geogebra and when i tried using it i had no idea how to.

Answer 37

:) i have to go, kids need a ride .... good luck with the geogebra specifics tho.

Answer 38

thanks..

Answer 39

@agent0smith can u please help?

Answer 40

try inputing 4/3 and see if it works is the best adivise ive got

Answer 41

@agent0smith

Answer 42

@dan815 plz help

Answer 43

No idea.