Question

Circle A has a center at `(8 ,1 )` and an area of `81 pi`. Circle B has a center at `(4 ,2 )` and an area of `36 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

Circle A and Circle do overlap.

Explanation:

Circle A, centered at (8,1), area `= pir^2=81pi => r=9`

Circle B, centered at (4,2), area `= pir^2=36pi => r=6`

distance between the two center points
`=sqrt((2-1)^2+(4-8)^2)=sqrt17 =4.123`

As the distance between the two centers (4.123) is smaller than the sum of the two radii (9+6=15), the two circle overlaps.