Question

Circle A has a center at `(2 ,1 )` and an area of `15 pi`. Circle B has a center at `(8 ,12 )` and an area of `9 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

No, the circles do not overlap
shortest distance between them`=sqrt(157)-sqrt(15)-3=5.65698`

Explanation:

Distance between centers:
`d=sqrt((x_a-x_b)^2+(y_a-y_b)^2)`
`d=sqrt((2-8)^2+(1-12)^2)`
`d=sqrt((-6)^2+(-11)^2)`
`d=sqrt(36+121)`
`d=sqrt(157)`

Shortest distance between the two circles `=d-(r_a+r_b)`

`=sqrt157-(sqrt15+sqrt9)=5.65698`

Let us see the graph of the circles `(x-2)^2+(y-1)^2=15` and
`(x-8)^2+(y-12)^2=9`
graph{((x-2)^2+(y-1)^2-15)((x-8)^2+(y-12)^2-9)=0[-20,30,-10,16]}

God bless ....I hope the explanation is useful..