Question

Circle A has a center at `(7 ,5 )` and an area of `92 pi`. Circle B has a center at `(9 ,2 )` and an area of `14 pi`. Do the circles overlap?

Answer 1

They will overlap,practically smaller one will be inside larger

Explanation:

Given
Area of 1st circle `=92pi=pir_1^2` , where `r_1`=radius of 1st circle
Hence `r_1=sqrt92`
Again Area of 2nd circle `=14pi=pir_2^2` , where `r_2`=radius of 2nd circle
Hence `r_1=sqrt14`
Sum of their radii `S=r_1+r_2=sqrt92+sqrt14`

Now the distance between their centers
`d=sqrt((7-9)^2+(5-2)^2)=sqrt13=`
S>d => They will overlap,practically smaller one will be inside larger one because `r_2-r_1>d`