Question

Circle A has a center at `(1 ,3 )` and an area of `18 pi`. Circle B has a center at `(11 ,7 )` and an area of `54 pi`. Do the circles overlap?

Answer 1

Yes, the circles do overlap.

Explanation:

Circle A, center (1,3), `r=sqrt18`, `(pir^2=18pi => r=sqrt18)`
Circle B, center (11,7), `r=sqrt54`

distance between the two center points
`=sqrt((7-3)^2+(11-1)^2) = sqrt116 = 10.77`

As the distance between the two center points is smaller than the sum of the two radii `(sqrt18+sqrt54 = 11.59)`, the two circles do overlap.

Here's an image of the two circles