Question

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Circle A has a radius of 3 inches, and circle B has a radius of 7 inches. Prove that the two circles are similar.

Answer 1

So, first, ask yourself this, are all circles similar?

Answer 2

nope

Answer 3

?

Answer 4

ok, let's start here then: what does it mean for objects to be similar?

Answer 5

same size shape and numbers

Answer 6

@FibonacciChick666

Answer 7

check your definition again, You are confusing it with another term called congruent

Answer 8

so similar means that they have similar shape and size etc but congruent means exactly the same number

Answer 9

@FibonacciChick666

Answer 10

yea, so a good way to think of similar is that it is just a bigger or smaller version of the same exact shape (ie you can increase the size of the smaller shape by some constant to get the bigger shape)

Answer 11

oh okay so how can i use this to answer this question?

Answer 12

@RedNeckOutLaw

Answer 13

well, do all circles look the same? do they have the same number of degrees? can you multiply 3 by something to get 7?

Answer 14

nope

Answer 15

I think you need to look at your definitions again

Answer 16

how many degrees are in a circle?

Answer 17

360

Answer 18

i was answering the last part of ur question. when u said can u multiply 3 by something to get 7

Answer 19

that is also incorrect to say no

Answer 20

but yes 360 degrees are in a circle

Answer 21

but how? u cant multiply 3 by something to get 7?

Answer 22

what is 7 divided by 3?

Answer 23

2.3333

Answer 24

so what is \(2\frac{1}{3} \times 3\)?

Answer 25

okay you can do that but you werent specific i thought u were asking about a whole number??

Answer 26

7

Answer 27

No, a constant does not have to be a whole number. It can be anything. In fact scaling(what we are talking about here) can be any real number

Answer 28

gotchaa..okay so wht do i do now?

Answer 29

@FibonacciChick666

Answer 30

So, are the circles similar?

Answer 31

mhm

Answer 32

What is the definition of similar? does it follow from the definition that all circles are similar? explain why and tadaaa you have your proof

Answer 33

thank you

Answer 34

np

Answer 35

Move the circle so that their centers coincide. Both circles have the same center and the same shape. Any radial line drawn from the center to the circles is always in the ratio 3:7 all around (360 degrees). The outer circle is just a bigger version of the inner circle or the inner circle is a smaller version of the outer circle. Therefore, the two circles are similar.