Question

Circle A has a center at `(8 ,1 )` and an area of `64 pi`. Circle B has a center at `(14 ,8 )` and an area of `48 pi`. Do the circles overlap?

Answer 1

Yes, the circles overlap.

Explanation:

Area of Circle A = `64pi`
Radius (Ra) = `pixx(Ra)^2=64pi => Ra=8`
Area of Circle B =`48pi`
Radius (Rb) = `pixx(Rb)^2 = 48pi => Rb=sqrt48 =6.928`
distance between Circle A and Circle B (center to center)
`=sqrt((8-1)^2+(14-8)^2)`
`=sqrt(7^2+6^2)=sqrt(49+36)`
`=sqrt85=9.22`
As the distance between the two center points of the circles is smaller than the sum of the two radii (Ra+Rb=8+6.928=14.928), the two circles do overlap.