Question

Circle A has a center at `(5 ,12 )` and an area of `81 pi`. Circle B has a center at `(1 ,2 )` and an area of `16 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

Both the circles overlap as sum of the radii is greater than the difference between the centers

Explanation:

Radius of circle A `r_1 = sqrt ((81pi) / pi) = 9`

Radius of circle B `r_2 = sqrt((16pi)/pi) = 4`

Distance between the centers of the two circles `d = sqrt((5-1)^2 + (12-2)^2) = sqrt 116 = 10.7703`

`r_1 + r_2 = 9 + 4 = 13 is > 10.7703 (d)`

Both the circles overlap as `r_1+ r_2 > d`