Question

Circle A has a center at `(5 ,7 )` and an area of `56 pi`. Circle B has a center at `(9 ,2 )` and an area of `44 pi`. Do the circles overlap?

Answer 1

We have to compare sum of the radii of the circles to the distance between their centers.

Explanation:

`A=pir^2->r=sqrt(A/pi)`

Circle A:
`r_A=sqrt((56cancelpi)/cancelpi)=sqrt56`

Circle B:
`r_B=sqrt((44cancelpi)/cancelpi)=sqrt44`

Together: `r_A+r_B=sqrt56+sqrt44~~14.12`

Distance between centers:
`D^2=(7-2)^2+(5--9)^2=5^2+14^2=221`
`->D=sqrt221~~14.87`

Conclusion: they do not overlap.