Question

Circle A has a center at `(5 ,3 )` and an area of `54 pi`. Circle B has a center at `(7 ,8 )` and an area of `15 pi`. Do the circles overlap?

Answer 1

**Let Radius of 1st circle be `r_1` and 2nd circle be `r_2**`

`pixxr_1^2=54pi =>r_1=sqrt54=3sqrt6~~7.35`
`pixxr_2^2=15pi =>r_2=sqrt15=3.87`

The distance between the centers of the circles
`d=sqrt((5-7)^2+(3-8)^2)=sqrt29=5.39`

Here it is found `d cancel(>=)r_1+r_2` So there will be overlap