Question

Are circles with the same center always the same size?

A) yes, if they have the same center then they are the same circle.
B) no, it is not possible for two circles to be the same size with the same center.
C) sometimes, if they have the same center and the same radius length they will be the same size.
D) sometimes, if they have the same center and the same chord length then they will be the same size.

Answer 1

Option C. sometimes, if they have the same center and the same radius length they will be the same size

Explanation:

we have two cases

First case) Two circles of the same center and same size (length of radius)

example

`(x+5)^(2)+(y-4)=15^(2)`

Center
`(-5,4)`,
`r=15 units`

`(x+5)^(2)+(y-4)=15^(2)`

Center
`(-5,4)`,
`r=15 units`

Second case) Two circles of the same center, but different size (length of radius)

example

`(x+5)^(2)+(y-4)=15^(2)`

Center
`(-5,4)`,
`r=15 units`

`(x+5)^(2)+(y-4)=20^(2)`

Center
`(-5,4)`,
`r=20 units`

therefore

sometimes, if they have the same center and the same radius length they will be the same size