Question

Circle A has a center at `(5 ,8 )` and an area of `18 pi`. Circle B has a center at `(3 ,1 )` and an area of `27 pi`. Do the circles overlap?

Answer 1

The circles overlap

Explanation:

the distance from center to center
`d=sqrt((x_a-x_b)^2+(y_a-y_b)^2)`
`d=sqrt((5-3)^2+(8-1)^2)`
`d=sqrt(4+49)`
`d=sqrt53=7.28011`

The sum of the radii of circle A and B
`Sum=sqrt18+sqrt27`
`Sum=9.43879`

Sum of radii`>`distance between centers
conclusion: the circles overlap

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