Question

Circle A has a center at `(2 ,3 )` and an area of `12 pi`. Circle B has a center at `(7 ,2 )` and an area of `64 pi`. Do the circles overlap?

Answer 1

Both the circles overlap

Explanation:

Circle A radius `r_1 =sqrt(( 12pi) / pi) = 2 sqrt3 = 3.4641`

Circle B radius `r_2 = sqrt((64pi)/pi) = 8`

Distance between the centers `d = sqrt((7-2)^2 + (2-3)^2) = 5.099`

Sum of the radii `r_1` & `r_2` ( 11.4641 ) is greater than the distance between the centers d (5.099); hence the circles overlap.