Question

Circle A has a center at `(2 ,2 )` and an area of `8 pi`. Circle B has a center at `(13 ,6 )` and an area of `54 pi`. Do the circles overlap?

Answer 1

No, they don't overlap.

Explanation:

I start calculating the radius of the two circles.
We know that `A=pir^2` then `r=sqrt(A/pi)`
The radius of the circles, that I will call respectively `r_1` and `r_2` are

`r_1=sqrt(8pi/pi)=sqrt(8)\approx2.83`
`r_2=sqrt(54pi/pi)=sqrt(54)\approx7.35`.

If the distance between the two centers is bigger than the sum of the two radius, the two circles will not overlap, otherwise they will overlap.

The distance between the two centers is

`d=sqrt((2-13)^2+(2-6)^2)=sqrt((-11)^2+(-4)^2)`
`=sqrt(137)\approx11.7`.

The sum of the two radius is `2.83+7.35=10.18` and `11.7> 10.18` so the circles cannot overlap.